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PO3Altl L ct4cTEMAr[3Aqlg TAv3ArAnbHEHHg oAKTIB I METOAIB
NTAHIMETPII
$ 1. Onopni Qaxru nnaniwrerPn-
Teruaruqni saBAaHHq E...
8.") Js.
V pinno6egpeHoro fipsMorcyrHolo rpr{KyrHuKa 6icenrpuca. onyrleHa na rinoteHyay'
e Me,qiaHoro. Me4iaHa, trpoBeAeua...
8. a) 16 cm. f,IHIqo r{BaApar onficaHo HaBKoJao RoJra'. To cropona r{Baaqpara AoprBxro€
4iaruerpy Ho.na. [on:rcr,rua r(oJr...
3)
4)
PisHssssrpauoi-AJ3:
r-rt
-a-at .
Iz-rt Az Ut
PieHssH,E noJra B qeHrpoM (a,'bJ i pa.4iycoM r: (.r - a)2 + (A - b)': P...
I
a)Y ACNB: CN =
rAC = 1,6 (cM);
BC : 4,8 cu; ro,4i BN = ,F,o' + l,z" = '125'6
= f,6J10 (cu).
6) V AACB: AC = 3,2 mr; CK =...
s) 3Hafi4euo Ha rreptrenArrnyJrspi roqry B, siAAareHy ni4 rounn A Ha 6 cM'
LABC
- ruynauuii: AB : 6 c.u: BC,
BH. Bilcora. ...
31. Hexaft y rpaneqii -43CD AB : CD : 13 cru, BC :
flpoue4euo BH LAD, AII -27 -^11 = 5 (cu).
2
B LABH (ZAHB : so") cos/A= ...
41. Hexait roq:ra M(x; O), rcai MO' : (r - 0)' + (0 - O)'z : x2, M P2 : (x - 2)t + (0 - 3F :
: x2 - 4x + 4 + I : x2 - 4x *...
Or.nre, 4iaroua;ri tpaneqii nepernrrarorbcg i roqrcoro [eperr,rHy gi.nRrr,cR y ei4no-
urenni 1 : 3.
Bi0noai}u: L : 3.
55. ...
p -
7 + 23 + 30
= z2; hl =
ft ' eua+- 80x64 - tL)ga - %);
nl 2, .8, .82^.b5. 4I
. h = 9 JOS5.J6
"*.go' 15 '"":"" ""'
61. H...
B) yAAcr: cD:LBcl*,AC:20cm,AD:2:_ew,togi p= 1'3+29+2L
=27 (cv,
S*,,=,lir.A 7-=3.7.6-126 {cn2); r =!#-+f,rca.
Bidnoaidu: ar...
87. J{nrqo m = d + 26, ro lfil= Jrn' = J@. r6f ='td 4d6 + 46' =
= 'rE + 4di | + r" - .tTa-b - 8.
Crarapnzfi 4o6yror a5 -la...
125. flxuope6pory6a a,V:43:8 cm3, rogia:2 clrn' S""".:642,
rogi S : 6 . 4: 24 (cv2), Bi)noai)b: 24 cM2.
$ 4. Axciorvrn cre...
BiApigrcy -RB; rogi ryaus DDTATA
- no ni4pisny MP; rpaxs CC.DtD
-
no ni4piexy
N-R. fl'aruxytsux RNMPB
- nepepia rcy6a nror...
181 . Hexai y rpsMonyrHoMy napa;re;reninegi ABCDATBTCIDI AD :6 cwr, DC : 6 cu,
DDt:8cluiM - cepe4unaAD, T
-cepegnnaDC,K
* ...
197. C:ria trJrorr{rHr4 fiepepisy na nparvriii -43 - roqna X, na npruifi BC
-
roqxa Y,
199. Ciqsa nJrorqlrna neperrrHae nJ...
EF a MY : S, PN a FK : ?. To.rrcrl S i ? ralexaru o6ovr n.norqranaM' orrrce' rrJro-
ururrr4 rreperr{Harorbcff no npswrift ...
Ocri.nrrcra pe6po nyda aiArM : MA: CtP: PC:3: l,
ro A-M=?o. ua=!.'44
f ,"^' sa
MN=NP=.la'+l ""1=:::
  4) 4
_sa,[, fftuo" B...
Ilo6yAyeuo nepepio rerpaeApa nrrou{rruoro (APK); (APK) a (ABC): -A-I{. Ilaorqnnu
(SPB i (APR marotr cninrny touxy ? u n.no...
ripfiMifiA1B1 i M, e ArBt. Branonaeuo napaJIeJTbHe rrepeuecenH,fl nigpisxaArBr y Ha-
npami .4-4, na ni4pison -4Ar, o,4eprc...
236. 9orupuxyruux AtACCt
- tpaueqis,
oo, - cepegua .ninia, oo, =
&:cC', ari4xu -AA' +
'2
+ Ccr : 2AO. V rpaneqii BTBDDI OO...
3a eracrueicrrc rpaHslrrtrBHocri MN ] PK. {epea napa.ne:rr'ui npami MN i PK rron*ra
ilpoBecrr nrrorquuy (M N P), ro1i M e ...
xt,z = '
rt,z
fE
I a a|'l
,2a!2oJ7 _l 2' 2
4 | o a.,17
l-:- *r,-<0.
12 4
-Zotrlio" +Zlo"
ornte, AC ="Qvr-r),
"*
=t +!+i="'...
LAA.C M
-
cepe4fiHaAAr,
-
Mo ll A,c, roii (ttnn) e,c.
Mo = ! 7..C, Mo = !; so . oJ2, a" a
- cropoH
2' 2
Fof* o,trt, u{ro u...
i LA.OB1. Bouu pinni Ba ABoMa croponaMr{ i xyrou uiuc nramu (AO :40, BO : BQ
Ba yMoBoro, ZBOA: ZBtOAl ax neprnra;rr'ni).
"...
At)'=25+64-2 a t;. AD2:r2g, AD-u1729 ct..
,flxu1o y traparlerorpaMa ABDC /ACD: L20", ro ICDB :60'' Is ABCD (BD : AA :
: 5 ...
ls MBD (ZBAD :90") BD -- JAu AD' , BD =
p*o* =ir*", =
fr,
o"nin * P6vNr i Paooc: k'
Sourr i Saarc : h'i S*** 64=4.
Bidnoei...
10 gdz geo_b
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Transcript of "10 gdz geo_b"

  1. 1. PO3Altl L ct4cTEMAr[3Aqlg TAv3ArAnbHEHHg oAKTIB I METOAIB NTAHIMETPII $ 1. Onopni Qaxru nnaniwrerPn- Teruaruqni saBAaHHq E TecroBii OopMi l-lpnmi i ryru 1'n)HaSa6orra4.Ilpauirran.noulurritrepeTzHaloTbcEa6onapa.ne'rrlrri.,flrrqontllx. Tr4HaroTbcg, ro poa6ttnarorr nr,rotrIr4Hy sa 4 qacrunui SKLIIO [apalTeJlsni, ro na 3 untr .T}l]lTI. 2. n) 50". Hexaii ogran xyr .r", rogi 6i:nurufi (r + 80)"' Cyua cymi:*cHzx nyrin 180"' ToAi x +rc * 80 : 180, gsi,qxu 2x : LOO'r : 50. Ornce, nenurufi xyr 50"' s al] b..{ri npami, fiepneuArlxyJr,Epni 4o rperroi upfiMoi, napa'renlni uint co6oxr s) 30'. Hexait a ll a i c - civua, A : b a c, B : a o c' Hexafr IEBA: 60', BC - 6icexrpmca ZEBC. 1 Tofi ZABC = ! ZAne, ZABC : 30"- lcAB : 180" - IEBA (eHytpirrrui onilo"topo""i npfi napaJrerbHr'Ix trpflMnx i ciunifi), zcAB : 180' - 60" lcAB : 120". v LABC ZC : L80 - /ABC - ZBAC, lc: 1a0'- 30" - 120" tc :30"' 5. a) 6' r) 7. 6) 8.6) 9. 6) lO, 6) 6. Hexafi na ogxifi etoponi xyra O poavrirqeni rouxr'r A, B, C D; 'l,l.a 4pyriE * At, Bt, ct i D,, Ae AA,ll B4ll cc,ll oo'; AB : 2, BC : 3, CD : 5, ArDr: 2O. Megia:ra rpraxyruur{a poa6unae fioro na gna pianone.rr Htrlrvt s pinuurtu n.norqatrv), .(la rpzxyrnr.rxa ai crop 2(a2 +b2-c"[poBe.qeHa Ao cropoHn c, ,4oprBHroc ^; = -' -z-- Yci tprz 6iceitrplrcu rpr,rlryruzRa rrepernuarorbcfi n ogu ca inu,eanpon mpurcAmHurca. Inqenrp rprrnyruurca e r s ganufi, Tpr.rryrHuK, Bicercrplrca rprxyrnrrxa no4i,rae nporulerxry iioro crop qifiui nprzleuuM cropoHaM. .{"rra rpz*yrurzxa ai cropon 4abn( o - c npoBe,rreHa 40 cropoHll c, AoprBHrce l: = @ + b), ' . Vci rpr.r Bvcorrr rpl4KyrHHKa neperr.rHarorbcfl B oAniii opmoqerlmpoJtr. npuKAnlHurca. ,(la rpuxyrHzra ia cro flpoBeAeHa Ao cropoHu c, 4opienroc o" = 4p(p - al(p-- t- 1, 6) 40'. Cyua xyrie rpriryrurzrca 180", ro,qi 2x-l 3x + nporopqifinocri rcyrin; 9* : 180, x - 2O; naftuenrulrf 2. 6) 90', Ocni;rr,nu r1afi6irrurfifi auyrpiurnifi xyr rpr4xyr a sram gosui[rsiri xyr 6yae nafimeHrunu. 3. 6) Jd 4nn2. fkoula pinHocroponnroro rpr.rxyrHrrKa t="+, ro.qi s=af ="6 to*,r. 4. a) 3 cu. 3. 4. 3a yaaramrienoro reopeMo$ @a.neca, flxrqo,4-B : BC : CD : 2 : 3 : 5, rogi ArB, t BrC, : CrD, : 2 : 3 : 5. Hexafi r - iix roe@iqient nponopqiftnocti, rogi 2x'l 3x + 5r - 20; r:2.Orxe,BrCr:2 3:6. Bidnoaida: 6. TplrKyrHxKl4 AB BC. CD 48 B,C, CrD Ba Hac,ri4xov B TeopeMr.r cuHycin, ,ACr= = 2R,' sin lB (oJIa, olucaHoro HaBKoJ'Io rpuxyrnzna, ro4i R= 3 =3 (cml. 2 sin 30" 5, 6) 6,5 cnr. 4e.R - 2 iii ,jiXl ,'d' iir irt V npsnroHyrnoMy rprrxyrur4xy uaitmenuroro rue4iaro ue4iana, npoBe,qeHa go rinorenyar. i gopirnioe ii n no.na). V npfiMoxyrnoro rpr{r{yrHnrca s r(areraMrr 5 c roAi nneaiana 6,5 crra, 6. a) 4. Hexafi y A,ABC npone4euo cepe4ni risii MN, NK, MK /ABC: lAMK: ZCNK (nnyrpilrni o4nocroponni n pa,rerbrrrx np,ffMrrx i civnzx). IMBN : ZMKN (npor ni xyru raparrerrorpaMa MBNK. IBMN : IBAC : I (nnyrpinrui o4nocroponni rrpu napaJreJrbrrzx i ciqnrx). ZMA-I(: IMNK (nporu.nencni xyrrz rapa,'rerrorpaMa AM LMBN : MMK : AKNC : ANKM N LABC (aa ABoMa r,ru). Orxe, Eorr{eH B yrBopeur,rx rplrxyrnrznin nogilnuf Maeuo 4 napH no4i6Hux rplrxyrnaxia. 7. r) s. p :;:iiiiili;;iiiiiiiiiii: TEOMETPI9 Eeae F. It. ra ix. t-tpoe Bnacrrsocti gonilrnoro rpr{nyrrrr$a Cyrrna nnyrpimnix xyrie: o + B + y - 180'' Teopema rcocunycie: a2 : b2 I c2-2bc cos a. Teopeua cunvcis: -:- = -!- = -!- = zn.--"-'---- sinc sinP sinY rDopny,rn nnouli rpurcyrnnrca: S = lrtO" = lln, = )rn", S = )aO s:'n l : S - ff : s = rp,se o =tTt s = filp - o)(p -b)(p - ct. Vci rpn me4ianu rpr4rtyrHrlxa neperr4Harorbcff a o4niii rouqi, Rxa rraol{Baerr'cs qeHmpoJw Mac mputymHuna. le:rrrp Mac rpunyrur'rrta no,4i'nae Horxny ue4iauy y siAHouenni 2 : 1, paxyrouu ri4 repurianrz rplrxyrrr4xa' 856 ::::i: rEOMETPIS Eees f. fl. ra ir. flpoQinux14fi piBeHb::i:::i;i:i:i:i:ii:i:i:i::::i:i::
  2. 2. 8.") Js. V pinno6egpeHoro fipsMorcyrHolo rpr{KyrHuKa 6icenrpuca. onyrleHa na rinoteHyay' e Me,qiaHoro. Me4iaHa, trpoBeAeua go rinorenysn, 4opinHroe no'loszHi rinoreaysra' ,o6ro 11io Js. 2 9. r) 21 cn'z. IlrorqyrpuryrHtr(aMo)fiHasHafituaaSopuyloro S - aUsiny (y xyr nixqzull 1 croDoHaMu). S-l 6 14 sin30'.21 1cm';.'2 1O.r) 2:3. II;rorIi noAi6irzx rpuxyrnrzxir ni4noCarr,ca sft KBaApaT nignoueuna ix cropis (xsa{- par xoe@iqicHra no4i6eocri). f - t' u 3 9oruplrryrxuxu 1. n) 4. lni oci npoxogsrb qepe3 giaroHali KBaApara' 4ri iHui qepes cepeAuHrr [po- tz.nexcuux croPiH. 2, 6 7 cv. Cepegns ;riuic rpaneqii 4opinuroe niecymi ocnon' 3. r) 3 clr. flinnepuuetp8cu, roAiApyracropona8- 5:3(crt)' 4, e) 4O":140". Cyva nyris pom6a (fiH i naparerorpaMa). nphrer;tux 4o o4uiei cropo- uu, 4opinnroe 180'. flnufo xoeSiqienr nponopqiinocri Hyrie r, ro qi nyru 2x"' 7x.'logi 2x i 7x: 180, ;r : 2O; 2x : 4O, 7x : l4O. 5. a) 1o cu. I Hexafi y npfiMor{yrHuny ABCD CD: 5 cu, ICAD :3O": V LACD (ICDA:90') rarer CD ne:x<url nporu xyra n 30", rorvy AC 2CD, AC - l0 cm. 6. e) 8rE u'?. Hexait y pov6i ABCD BC : AC : 4 v' LABC - pinnocroponnifi, rogi ZABC : 6O". S*"o: AB ' BC ' sinZA-BC, S*,o- 4. 4 .sin 60" - AuE (no'). 7. a) | :2. Hexafi y npsMonyrHrrrcy,A-BCD nponegeuo 6icexrpucy A1{, IBA]<: IDAK. Tofi BK: BA. B Ilpoeegemo KKr L AD. S-u. = S*r.,, 3a yuonoro S*"o: 3S*" I{e rro:r.nrlno, aHulo KrD : -AX, a ornte, AD : 2A-I{t: 2AB. AB:AD:I:2. K1 8, a) 5 cu. flHuqo uorzpnxyrHl{ri e onucaur M HaBrcoJro Itora' ro cyuu fioro npor[Je]fi- 1 Hux cropiH pinHi, or:rxe,.4opinsrororr 1 20 cu: 10 clr. OcHi,rlrcn rpaneqia pieno- 2 6egpena, ro 6iqsa cropoHa 4opienroe I ro "* : 5 cn. 2 858 ;:::::: TEOMETPIq SeBo r. fl. ra ix. rlpoQinunui piBeHb i;:iiiiiiliiiiiiii{lii'i:: 9. 6) 120" a6o 135'. Hafi6i,rrnnu ia rcyrir nparvroxyrHoi rpaneqii e rynufi, y 2 pasu a6o nig npsuoro Hyra, a6o ri4 rynoro rcyra mennruii ni4 npnrroro Kyra, ro niu 4opieHroe 45", a (cyma xyrie, rrpnrerJrrrx 4o 6iuuoi cropoHr rpaneqii ,flrcrqo rocrprfi xyr y 2 pasr uenurrafi ei4 rynoro Hyra ny x", a BerxqtrEy ryfioro Hyra 2x": x I 2x: 180; x nyr gauoi rpaneuii 120' a6b 135". 1O. r) 6 cm. Hexait y porvr6i ABCD ZBAD : 12O", r Ocxialnz n porrn6i 4iaroua.ni e 6icexrpracauz rior D / 4u "1 "n',/ / D K? .zBAC - I .tZO" = OO.. 2 Togi IBAC : ZBCA: /ABC : 60", MBC - pinn AC : AB; AB =1. P^o,,, AB - 7..24 "*- 6 cv; AC - 6 cv. 4*'" 4 Kono i xpyr 1, a) n2 u. flonrxuHd xo,ra C : 2nR, iroro vnepri C'- -. n.2nL"= -='I" (Ml. 2 2, s) 2On cu. flroula rpyra S : nR2 :100n cu2, rnAi -R )rcuHa HoJra C : 2nR, C : 2n . 10 crra : 2On ctt. rii i,li .ii'i ii$ 3, r) 55'. Hexafi y xo.ni s rlenrpou O nponegeuo paAiyc n xinqnx fagiycin CA i CB, ge C' roqlca rreperrrny 3a ymonoro IAOB : L25". 3a n,racrusicrxl AorrqHux ZCAO : ICBO :90'. pr,rryrHrxa ACBO cyva nnyrpimuix nyris 360", I - 360. - (tcAo + zcBo + 44ozl:360" - 180. - t25 4. r) 120". Hexafi y pinnocroponuifi rpzryruzx ABC xo.no a qeHrpom O, Ldenrp nnzcanoro Rora O - roqxa neperr4ny licexr i CO rpuxyurzxa. Ocxi.rrlxu y AABC ZA: lC: 60o, ro - ,locA - 30". IAOC - 780" 2ZOAC - 120". Ocni.nsxra cropoHy AC BuAHo 3 qeuTpa BtrucaHoro nola rom AOC, ro ii nz4no nig rcyrou 120o. 5, r) 4 cm. V npanumHoro [recrurcyrnrzna cropoHa gopin IroJro HEoro lro,Ta. 'foAi nonra 4opieHroro ro !.rncu : o 6.n)4u. Hexaii nola s r{eHTpaMr{ O i O, marort nnyrpinuro y ro'rqi O, OA < O,4. 3a yrraoeoro OA: 7 yr, OrA: 3 "Io4iOOr:7 - 3:4 (rvr). 7,6) I6n m2. Ilron4a 6i.nsnroro orpyra S : n. 52: 25 MeHuoro - S' : tt . 3'? : 9n (u,). flrorqa ni,rrqa S,: S S', S,: 25n- 9n: 16n (ur). DA ffiiiliiiiittilli rEoMETPle 6eee r. n. ra ix. npoe
  3. 3. 8. a) 16 cm. f,IHIqo r{BaApar onficaHo HaBKoJao RoJra'. To cropona r{Baaqpara AoprBxro€ 4iaruerpy Ho.na. [on:rcr,rua r(oJra 3 4iarterpou d: C : nd, ssigx.r- d = 9. Togi d, =16n = 16 (crvr), i cropona rcna4para 16 cu. n It 9. s) 9 cNr. Hexaft y Ko,IIo 3 l{errrpoM O rfiuca:.c'o LABC' AB : BC : AC. V LABC 1A: ZB : lC, orxte, Ayrnl' Ha sfii crapalorr'cs qi nnrcaxi Hytu, pisHi. wAB : wBC : wAC- Ocxi.nsxu uAB + u AC : 6cM, ro uBC=1 O=3 (cu), aAoBlr{r4- na xoaa 9 cm, 2 1O. a) 6n crvrz. Il.norqa cer{ropa 3 qenrpaJlbHraM ryrom 60" / ' I Hu 60" = l soo". s"^: n-R'?, roAiAopiBHloe e5*e., ocRlrb 6 , ls^=1.-n.o2=6n(cu'/). 6"p 6 9" 6) 3A: 4r. l{eutp Ho:ra (0; 0), Pinnauna npfiMoi, rqo x-x. u-u.TOqHU: - xz-rr Az-Ut !,pyra rovxa (3; 4), roa; x -o - Y -o x - atr_o=ni,"=2,4x:3s 10, e) y : 3. I{enrp rco.na (0;.2), pa4iyc 3, ro4i 4oruvH neperr.rHac xo.no n 2-x roqirax, Berropu 1.6) (-8; t't. AB(-7 -r:12- (-3)), ,4ii(-8;15). 2.9 a.6 =o. 3. a) (8; -7). 2F = f-+,,21, 34 = Qz';S), m(-4+72i2*9 c. a 2J5. l,i' = [-2fu 4' = J+ r+n to = zJs. 5, r) (4: -16). BianosiaHi xoopgraHaru rco.nineapuax nexr 4 = -q, ro4i no,rineapH uir (4; -16)._16 6. n) 0. nC+ dn+ OA+CD =(BC+ Cil ,OA+ ttf)= 7. 6) 60". (i 6 =lal.lal cos(a, a); cos(ri. a) = ,r:h, cos 8, n) 3. Bexropu [eprreuAnnyJrspni, ariqo ix cra.nnpnra Iogi -2 .I * 6rn: 0; 6m : 18; m : 3. 9. s) -8.5. a = {, x =3'7 =?} = -! = -".u.' -6 7' -6 -6 2 10. r) -b. Benrop BA nporu.terxnr.rfi po en, axulo np npoerqia EA naOy * -b. S 2. Mero,4'r posBtssyBaHHc nraHiMerpnqHhx 3ag Mero4 xoopgznar. Braxopucrann.E MeroAy rcoopAranar cnJr4 1) nnogarr 3pyrrHr.rM cuoco6ovr AeraproBy crrcreMy noopA 2)yuony aagavi ra ii srcuoeox nepexJra,4arort Ea MoBy K 3)AosoA,firB a6o o6qlrc.nrotorr neo6xi4ne Ba AorroMororc e HOrO anapaTy: 4) o4epxanr,rii peoyJ'r brar Sopuylrorcrr, y repm i Hax sa4av Ilpr,r 4rolry BurcoprrcroByrorr rari @arcrra: 1) ,flrcqo sa4ani gni rovru A(xr; y) i B (xr; yr) cnoiMu Koop nigpiaxa AB o6qucnroerrcs Ba OopMyroio: lesl= ,UQ, - 2) .flxrqo ro.rna C no4inae ei4pisox A-B y nignourensi AC Harr,r roqlcn C(x; y) o6wcnrororbcs sa ([oply,rarvrr: r=t:*1*',r=u'-+^u'.To4ixoop4nnarr,rcepeAr4Hrrni4pien 1+1. " l+L aa dopuvraurri x = rrl xz . y = a'!-!z . 2 '" 2 KoopAraxaru sa nnouluxi 1. 6) (4; 1). Itoopgzirarz (x; y) cepegunu nigpiara e ninqauu (xr; a) i (x"; yr) o6wc- r,rrororbcn aa abopMy,laMu, * = {t;:, g = yLj-!' . Tori r = t -7 = 4,, = -3,* 5 = 1. orxe, Koop4r'IHartt cepeA[HI{ ei.qpiaxa (4: 1)' 2"2- 2. e) AC = Ct -* + <z - q,sf = t6;z,u =,ltt,zs, BC =,!@-27" +16-4,5y =,10;z,zs = ^11t,%, rofiAC: BC. 3. s) (2; 5). V rovnu (2; 5) x : 2, y : 5, ro1i 2x + a : 2' 2 + 5 : 9 * 7, ovxe' (2; 5) He HaJrexrrrb nParriii 2x + Y : 7, 4, s) 29 - x: 2. V napalenr,Hnx rrpnMnx xyroei xoeabiuieuru pinni. V np:rmoi x+2 1 I 1. 2g x:2, u=^;!=i*-'mvronufiKoediqicgr r'nxi vnpamoi a= rx+5' 5. e) 135". x+ A:5, A: -x * 5.,{auanpfiMa - 6icercrpuca IIiIV xoop4zHarl{r4x vneprefi, nepeuecena napaJreJrbHo BBAoBT{c Oy na 5 oAr4ur.rrlb yropy. 3 AoAarHr4M Ha- np.fiMxoM O.r yrnoproe rcYr 135". 6. n) (0; 2',1. x2 + (a - 2)', - 8 : 0; (r - 0)' + (y - 2)' - 8 : 0; qeurp (0; 2)' 7. r (6;0). V toqxpt M xooppnuaru (x; O). Toni MA2 : (5 - r)' + (4 - O)'z : 25 - 7Ox't xz * 16 : x'z - IOx * 4L; MB2: (2- x)2 + (l- O)":4- 4x t x2 !l: x2 4x + 5' Ba ymonoro MA: MB, MA2 : MBr; x2 - 10x * 4 : x2 - hc + 5, 6x : 36, x : 6. Or:xe, rovxa M(6: O), B. n) r'? + y" : ?5.1{e'rp xo,ra o - cepesnna Aut ol+t f) . oro, 0), nsaApar pa4iyca n': (4- 0y + (3 - 0)': tO + 9:25. 'fo4i pinnnnHa ronatc2 + A':25' 860 ll{: reOurerplg Eees F. 11. ra in' IlpoQinsxrr piBeHb i:jiilitilfii:li:;i{i*i iil ii I ii:::ii:{ilttiiil:f; TEOMETPI9 Eees F. Il. ra in. ItpoQi
  4. 4. 3) 4) PisHssssrpauoi-AJ3: r-rt -a-at . Iz-rt Az Ut PieHssH,E noJra B qeHrpoM (a,'bJ i pa.4iycoM r: (.r - a)2 + (A - b)': P. 1. Tpz npnui, nponegeHi rrepes oAHy ror{Hy, po36r4Barorb trrorrluHy Ha 3 napu Beprrr- KaJrbHr,rx, a oTlrce, piBHax RyriB. Ilpunycrurvro, qo )t(oAeH is 4zx xyrin He MeHrrrrrfi aa 61o, ro6ro Korr(eH i3 HyriB 6i,'rbilufi a6o AopiBHIoe 61'. To,4i cyMa Bcix 6 yrnope- nux ryrin 6i.nr,ura a6o 4opinuroe 61' . 6 : 366", rqo HeMor{rrlBo, ocrci,rrxra ix cyma 360". Orxte, Harxe npr4rryu{enHri HenpaBurbse i o6os'seroso e Kyr, meuurufi ea 61", a, ocrcirsxz 4Jrs Hboro e Beprr.rxaJr,HrzI? (i pinunfi), ro npuHafiuni ABa B yrBopeuux nyrir menrni ea 61'. IIfo fi rpe6a 6yro goeecru. 2. ,flrcqo xoe(pirlieHr rponopqiiiuocri Hyrin r, to niryrpiurui r{yru .r, 2x,3x, a ix cyma 180'. To.qi x * 2x i 3r : 180, t : 30. Hafi6iasnrufi ryt 3.r : 90, a orxe, rprrnyr- nzr npRuoxyrnufi. Bi4noai}t: npsuoxyrnufi . 3. Cyma aoeHilxuix Hyrin rpurcyrnrrxa, B3srux tro oAHoMy npra aeprnuui,4opieuroe 360". Sossiusi xyru 2x, 3x, 4x, Ee r - xoe@iqieut nponopqifinocri. 2x i 3x + 4.r : 360, x : 40, Hafiuesunfi sosuiuHiii xyr (2x: 80") - 80". Haii- 6i,rruuu euyrpiuxiu xyrom 6yge xyr, cyvlir+*urfi s Haiiuesmnu soeuiuruiu. Orrxe, uyranrafi xyr 180'- 80' : 100'. BiOnoaiOu !OO". 4. flxqo npnunfi rcyr 4irnrrcn Brrcorolo i wIe,qiaHoo Ha 3 pisHi qacrhHfi, ro xoxel i: nzx 30o. I{yr uirx xareroM i eacorolo 30'. Kyr uix quu )+(e HareroM i 6icexrpacoro npsMoro *yra45'. Orxe, xyr mix 6icexrpzcoro i sl{cororc: 45o - 3Oo - 15o. Bidnoaidu: 15" . 5. ,{o6ygyerrno qorrrpuryrHnK ABDC. flxt4o y qorupunyrH14na 4iarona;ri neperzHarorb- 6) V LCAM i ACBN: AC: BC, ZC - cninrrt:aft, ZC orxe, LCAM - ACBN 3a cropoHolo i npuaer,rrzun g II{o ri rpe6a 6yro gonecrn. 8, Ilnan nodydoeu. Ilponegeuo: 1) npauy a ra o6epeuo xa airt rourcy If (riHia ocuoez rcyrH rxa): 2) nepneu4nrcy.nap B roqxlr I{ go npauoi a (lirrin en TptrKyrEERa, npone4enoi go ocnonu); 3) eig rcivru -FJ Ha nepren4zny,rapi ni4naa4emo ni4 BH :6 cm; 4) aa gorouororc rlt4pnyJ'rs anaft4euo na nparrifi a 4 roqxuBsa8cu. Y MBC AB : BC :8 cv., BH: 6 cu. 9. Ilnan no6g0oau. flo6y4yeuo: l) npauufi xyr C; 2) ua o4uiir fioro cropoai ri4xaa4euo aigpisox CA: 3) ua inrrouy Hareri aa AolroMotoro rlr4pnyJrfi anafige ei44aleny ni4 rovxra A ua 6 cu; 4) Ha npoueni CO nigxaa4etro ni4 rovna O ei4piaon ni4piexy OC s 4pyroro 6oxy ni4 roqrcu O, y LABC ZC :9O", AC : B cm, AO - vesiaua, AO : 10. Ilnan nodAAozu. 'flo6y4yeuo: 1) e xiHrl;r A nigpiarca ,4-B lpone4er,ro npouinr nig ro crplru nyrorr 9o,43; 2) na npomeni ni4n,ra4euo Z pinnr,rx ei4pisxie 6y4r-axo ,qots)nrrHr AA, : ArA": AAr: AA^: AA": AAu =Mi3) s'egnaeuo ei4pienom ro.rtiu Az i B; 4) uepes rourr-r Au, As, A4, Ai, A,, A, npoee1er,ro npaiv napare:rrHi ArB, axi neperHyrbAB nignoei4no B roql 3a reopeuoro @aleca, A-8, : BrBr: B2BB: B"Bn: B^ cs 1 ToqItolo nepeTtrHy AlJrfiTbcJr HaBnur, To qez qorupr{rcyrHr{}c - napareJrorpatt, orwe, ABDC -naparerorpaM, A-B 1 DC, BD ll AC. a) Pocr.nsueuo LMAO i LNDO: AO - OD, IAOM - - lDON (aepruxa,rsHi), . MAO - INDO (suyr- ^ir ,i ii.-...... pinrni pisHocropouni npn AB ll DC i ciqnifi BC). To,qi LMAO : ANDO sa cropoHoro i npu,rerrrauu 4o nei xyrauu, orxe, MO : OC. 2) Ocxi.nucu LMAO : ANDO, ro AM : DN. 3) Ocximxu LMAO : ANDO, ro ZDNO : 1AMO. IIIo ft rpe6a 6y.no goeecrr.r. 6. 3a yuoeoro AC : BC, AN : NC, BM : MC. C1 To,qi -41r' : BM, NC : MC. / a)YMMBiLBNA:AB -cninr,na, MB:AN,ZNAB: IMBA -- / . (xyrn npu ocuoei pinno6eApeHoro rpuxyrHrxa). "A ' Tor.i LAM B - LBNA 3a ,rBoMa cropoHaMu i rcyrov mixr HNvu. I 7 6) v LCAMiACBN: CA:CB,CM :CN, lC *i"t""ti,-t"^t a Z g LCAM : ACBN oa ABoMa cropoHaur i xyrorvr mirx nrznu. III,o ii rpe6a 6y,ro gonecru, 7. 3a 'ryronorcAC.: BC, ro4i 1A: lB; ZCAM : IBAM : ICBN : .IABN. a Y LAMB i ABNA: lNAB : IMBA, INBA: IMAB, ,43 - cui.rura, rogi AAMB: LBNA 3a cropoaoro i npr.r.ner,rzurz 4o nei nytauu. A A62 i{::: |EOMETPI9 6eB3l. Il. ra in. flpoQinrxri piBeHb iii::::rl;:till:ji{i:l iiiiiiiiiii;iliil:i rEoMETpte Eees F. n. ra im. npoei
  5. 5. I a)Y ACNB: CN = rAC = 1,6 (cM); BC : 4,8 cu; ro,4i BN = ,F,o' + l,z" = '125'6 = f,6J10 (cu). 6) V AACB: AC = 3,2 mr; CK = i"" = 2,4 (cr*t); rosi At( = 'ts,r' - r,4'= JG = a (crw). n) V AABC: AB = $,2' + 4,8" = G3,r8 = r,ol[5 (crra). V npnrroryrnoMy rprztyrHrrxy me4iaua, npoBeAeua go rinorenysz, 4opiniroe ii no- 1 ,rogilHi, orn<e, CM = )an = 0,8r43 (cvrt. Bi}noei}u: 0,8'[5 (cu); 1,6{0 cu; 4 cm. 13. Hexafi y napaJrerrorpav,i" ABCD 6icenrpwca BK, ZBAI{ : ICBK, AK: 5 ciir, KD : 15 cm. AD : AK + KD, AD: 20 cru. ICBK : IAI{B (sHyrpiuHi pienocroponni npu BC ll ,4-D i ciuuiia BK). To.qi LABK : IAKB i MBK - pinno6e4pe- suft s ocsogoro BK' AB : A-I{ - 5 c*t. A P*"r: 2(AB + AD), P*"o: 2. (5 + 20) : 50 (cm). Bi}noei1a: 50 cttt. 14. Hexafi y fip,flMoxyrHraxy ABCD 4o giaroHali AC npoae4eno repnen4raxy;rap BfI i sexaia All : CH : 1 : 2. flxulo xoe(fiqienr ix nponopqiftnocri B * (r > 0), ro AiI : x, CH : 3x, AC : 4x. y LABC ZB - 90", BH - wtcora, flpoBeAeHa 4o rinorenyer' A To.4iA3'z : AC . AI{, AB2 : 4x' x : 4x2, 1l roili AB = r, = i.+x = jnC. II{o ii rpe6a 6y.no gonecru. 15. Hexafi y LABC BH LAC, BH:4cv, AB -: 6 cm, BC = 4G c*. ts LABH (zAlIB :90"): ,4-H = J An" - BH'; ilr = ^tE6 - 16 = zJs (crvr). 7a LCBH (LCHB - 9O'): cH = '[Ec" - BH',crl = r,(4.f6f - 16 = aG (cu). TosiAC : AH + HC, AC = 6J5 cu. = 1 aG .4 - Lz,fb @.''.S*. = iAC BH, Sffi, 2 BilnoaiTt : l2n!B cw'z. 16. Hexaii ocuonx rpaleqii a rrn i b u, a > 0, b > 0; cepegna.niuin a=15, b=5. 6 sittlA= BC "inz/.=!. "o"1A= AC . "o". AB 13' AB' Ls, zA = 4. tr za =Y = 2.4.. "AC-a n) sin lC : sin 90' : 1; cos lC : cos 90' : 0; tg lC 18. ,flHruo cnHyc o4Horo nyra 0,5Jd = f. t" BeruqnHa'2 urifr ocNoni). ToAi lcyr npu ueuurift ocnosi 180o - 60 rpaneqii, [prrJ'rerJrux Ao 6i.rnoi croponr4, - 180'. O 'ro Kyrr,r npfi ocHoBax pisni, orme, Kyrn trp[ snxuif uifi - no 120". Bidnoaida: 60', t20'. 60', 120'. 19. Ilo6ygyerrro npanrnfi xyr-4 i Ha fioro croponi ei4n.n Hzr1r, Ha 4pyrifi croponi xyra anafi4er'ro rouxy C, n .nena ni4 ro.rrclr B na ei4cranr 1 o4r.ruraqa. Togi /-B - uryrcauufi, ocxi,rlnra B npflMo(yrr{oMy M (zA:so') costB= #= T=t,t r,Ao'58 Toil /B - 60'; sin60'=;; tc60'= J3. t; Bi1noaida: Y; Ja. 2 17" Hexaii y LA-BC lC : 9O", AC : 5 c*r, BC :'l-2 cttt. Togi AB: 13 cu. a) sinrB = ffi, sinzn = ft, ".o"za = 99, cos lB = tglB= AC BC' tglB= 2O. llo6y4yenro rpxuufi tyr a nepruznoro A i AB : 5 oAr4glrrlb i AC : 1 oArrHr4qfi. Tovy a AABC (ZA : g0") ts ZC = 4, E zC =- AC' " i lC - uryxanrfi. 3a reopeuoro fligaropa, BC2 : AB2 * AC2i BC2:25+7:26; BC=Jr6. 51 Toni sin lC = -;: , cos ZC = - =-.'126 v26 51lJlOnOALdb: -i -. 126 .126 21, Ilnaa no6g0oau. a) Ha npamift a o6epemo roury 11 i nporegelro a nei KyJrfip Ao o. 6) Ha nprmifi a nig rovxu 11 no pisHi 6oxu ei4r.na4eu HA=Hc=l o-z tr*).n iiiiiittil{i:litt::.:il rEoMETPle Eees r. !-1. ra is. Ilpo 28 vti raP. lo s.. c. I 5 - 12 i3' B D K na iioro c 5_ = 1 a+b 2 3a ymonoro {a-b=10' la-b=lo. l2a'Bo, 1-' =ro: la+ 6=2st zd =to, Bilnolilb:15ui5u. i) 15 964 iiil: rEOMETPIS Seas F. n. ra ir. IlpoQinuxilfi piBeHb i:i:i:i:::i:i:li:::'ii:i:i:::::
  6. 6. s) 3Hafi4euo Ha rreptrenArrnyJrspi roqry B, siAAareHy ni4 rounn A Ha 6 cM' LABC - ruynauuii: AB : 6 c.u: BC, BH. Bilcora. coszA=ffi, "o"za=?=I 22. Hexafi cosZA: O,8; coslD : O,6. a) lA+ ZB:18O", lB:18O" - 14; coslB : cos(180' - ZA) : -cos.1A: -0'8; sitr lB - ^tf *", n = fi o,aa = o,o; sinzB 0,6 3 tp llJLa " cos, B -0.8 4' 6)ZD+ lC:18O"; ZC:1'8O'- lD;coslC: cos(180" -. D): coslD:-O'6; - 0,8 4 sinzB- Vl-( 0,6)'=Jl-0,36 0.8: tg-B= O.O=-a 23. 3a yuonoro si4omi,qni cropoHr{ i xyr mirx Hurrrz. ,{.ns 3gaxoA}r{egHs Heni4ouoi cro- poHu BlrKoptrcraeMo reopeMy xoczHyci s. a) AC2 : AB2 + BC2 - 2AB ' BC ' cos lB; AC2 : 32 + 82 2 3 8' cos60' : 9 + 64 - 24: 49:' AC : 7 cvr. 6) BCz : AB2 + AC2 2AB AC . cos 1A; nc' = (arE)" + 42 - 2' arE'' q' cos 45" = 7 2 + L6 - 48 - 4o; BC = 2l[b cu' Binoaidu: a) 7 cm;6) 2J10 cm. 24, Hexafi r xoedriqieHr nponopqifinocri cropiir, ro4i cropouu tpuxyrr;axa 7x,8x i 13r i sa yMocoro 7x l8x + 13r: 56, x :2.,{onxuHr'r cropin tprznyrnnxa 14 cm, 16 cm, 26 cu. Haii6i;rr,urufi Hyr o JreE{r.rTb nporz nafi6i:rl)]Iroi croponz TpltlcyrHl{rca. 3a reopemoro xocuHycie: 262 : 74' + 162 2 ' 14 ' 16 cos q, ., _ 142 +16'_ 26'z = _ l - rooi a : 120..3BrAHu cosd = 2.w.rc 2 Bidnoair)a: 72O", 25. Hexafi y raparrerrorpami ABCD BD : 12 cr'tt, AC : 32 cv, AB :'14 cm, To,ui BO : 6 cm, AO : 16 cnr, 4e O - rorrga rreperuHy Aiaro- 27, [:ze. puc. 4o aagaui 26. }{exaft y pou6i ABCD AC an-rp^"-^, AB=! 6,8=l,z (cv). Ao=!o", 4 *'" 4 2 3 LA2B (ZAB : so") Bo = 'EE - ,qo"; Bo .EJ' 4.8'- 6.r .z,r = 0,8.5 = l,b (cv). so",, . 1 AC.BD = AC.Bo, s*., = l.6 l,b = 2.4 2 Bidnoaida: 2,4 cv2. 28. Hexafi cropoHu naparerorpaMa aib,rocrpuir xy P:2(a + b):52, a + b:26,b:26 - a. S: ab 6O: a(26 a).sin 3O', 6O-a(26-14 +, 26a -2' Seigxu ar:6 a6o ar:2O, ro4i br:2O a6obr:6. a-6cv,b-2Ocw. flrorqanaparerrorpaMa S:a.h.:b.ho,aeipxu h- f, ," = !9 = s t"*r."h'20 Bi)noai}u: qropoHu 6 cm, 20 cM; Errcorr4 10 cu i 3 29. Hexa:ii v rpaneqii -A-BCD A-B : CD, BC : 8 cu, AD AD: 18 cm, BH LAD, BH eucora rpaneqii, Rxa 4opinnroe 4iamerpy BtrrrcaHoro ItoJra. Ocni.nrnr e rpaneqiro Mor+{Ha Btrucarn xono, roAB + + cD : BC + AD, AB + CD : I + 18 : 26 (cu), aos IBOA 2BO.AO 2.6't6 2' A lt.lii::iil: IBOA:60' (ryr uirx giarouanaMu traparlerrorpanta). 3 ABOC maeno: :..:iiii:ii:!:i: BC, : BO2 + AC2 2BO .OC . cos tBoc, :!!i.1:;ii:i:i BC2:62 +162 - 2.6 .16.cos(180'- tBoA):36 + 256 2'6't6'(-cos tBoA): tii;iiiii : zsz +e6 : 888; BC =2Js7; P*"o =2(74+2"ffi)- 4(7+"i67) (cM). ,:l:,iiiiii Bidnoeida:60'; n(7 - "67) "*.:i'i:i::li:l:: B -i;,iiii,ii 26. Hexait y pov6i ABCD roq$a neperhHy.u.iaroHa;reii o. AC ' l2 cvt' n BD -t6cv. s*, ,=Ior'BD, sM.D=) tr 16=96 (cv'?). , (4)" Y LAOB (1AOB :90") BO : 8 cvt, AO : 6 ctrt, I / roAiAB: 10 cnr. V Pa"r: 4AB, P*,,o: 4A cw. D Bi6noai0a: 40 cu; 96 civr'z' 866 l:id: TEOMETPIS Eees F. Il. ra in. flpoQinuxhfi piBeHb ii#;i:.::iiiiii:;l:'+i 'I A,B - CD =' .ZA = 13 (cm). 2 Bncorr pisuo6e4peHoT rpaneuii siaruuarors eir Hux Hsoi ocuoeu pieHi ei.qpiexfi. roti Atr = M -^BC ,''22 3 LABH (lAtrB: 9o') Br{ - ,,En' - dn', BH = To,qi paAiyc BtrtrcaHoro Hora 4opinHroe l-at - o "Bidnoeida: 6 cyt. z 30. Hexaft y AABC (lC : 9O") CK - 6icerrpuca, AK 3a eracrrreicrrc 6icexrpucu Kyra rpunyr'."" AC204 BC153 ,flrcrqo n - xoe@iqienr nponopqirluocri rarerin AC 4x, BC - 3x. Y AABC AB: AK + KB, AB: 35 cm, AB2: AC2 + 35'! - llx)t + (3.r). 25x' : 352, (5x2 : 35', 5x : 35, x : 7; AC:7 .4:2a (cu), BC :7 .3:21 (cm). s.^"- 1AC.BC. s^", =:-2a.21 -294 (cM,). 2^''2 Bidnoeida: 294 eM'?. i;:li:ilriili*t:ilii;::i TEOMETPI9 6ees F. Il. ra ix. flp to* sarefi, Ba Hac,ti4xom I TeopeMr,I lcocuuycrB, Bo2+Ao'-AB2 t4 62 +76'-142 | t
  7. 7. 31. Hexaft y rpaneqii -43CD AB : CD : 13 cru, BC : flpoue4euo BH LAD, AII -27 -^11 = 5 (cu). 2 B LABH (ZAHB : so") cos/A= + = +AB 13 3 LABD Ba reopeMoro xocnuycin BDz : AB2 + AD2 - 2AB .AD . cos /A, BD2 =132 +212 -2.L3.2L.1 = t6t + 441 - 210:4oo, BD:2o cw. 13 BiOnosida: 2O cv. 32. Cyva rcy"rin onyx.noro n'R'rrxyruuxa SE :180' (5 - 2). S; - 540', flr.cuo rcoe@iIlienr nponopqifiaocri xyrin - x, ro Benvq'fi:F.u nyrin 3r, 4x, 5x, 7 x, 8.r i 3.r + 4x 'l 5x * + 7x + 8x: 540; 27x : 54O: x: 2O, roai 3r : 60, 4r : 80, 5r : 100, 7x: 140, 8r : 160. Orrxe, ryru 60", 80", 100", 140', 160". BiOnoei1u:60', 80', 100", 140", 160", Bnyrpiurnift rcyr B npa- 180"(n - 2) Cropoua rrecrrrnyrr{vfia t" =:, ", = f = 3 (cm). Cropoua onr,rcanoro npaBfirbHoro rptrnyruflKa a" = p" - Ba", p3 = lSJa cM. s3 = $, U - {e "61' Bilnoaila: 18J3 cm; 27^/3 ctn'. 37. Hexafi pagiyc xola, oracaHoro HaBHoJro rrpaBaJrbHo caHoroBHboro -- r. R: au-4c,r, r=+, r= fl.norqa xinrqa S,. : So - S", S,,. : nBz - na : n(R2 S" : n(16 - 12):4n (cu'). Bi4noeida: 4n cv2. 38. ,flrrqo A(3; a), B(-}i 4), c(-3; -4), ro AC= G+3)' +(4+4)' =LO; BC= J1_3+O:L(4 poHaMrr 6, 8, 10 - np,fiMoltyrrruft e rinorenyaoro 10 gopinHioe noronltni go6yrxy xarerin, roAi S = f o Bilnoailu: cropoHrr 6, 8 i l; cM; nrroura 24 ." &,. 39. Hexaft y rpzxyrnr.rxa *43C A(7; 5), B(4; 1), C(-4; "(z r+.r+taM - cepeAtrHaAB; M 2-; 2 ), M(5,5; 3), rosi uesiana CM = Je+ - S,Sl" * tl - s (4-4 t+7 6)N - cepeAr4na nC; w[ ,j t;), N(0; 4), ro4i negiaua Ar,r = !/47 - 0'/' + (5 - 4)' = "6 /" -4 5+7 s)K - cepe4r,tra Aq Kl;r;), K(1,5; 6), ro4i ruesiana ,B1{ = G- 1,5)'+ (1 - 6)' Bi0noeiOt: ; rJi; 11 cn. ,4-D : 21 ctu. 811 a 2L 360" 33. I]enrpa.nrnrft ryr c' irpaBr.rJrbuoro rl-nyrunxa o = -.Brzrrb'oro z-r(yr*r,.*a 1] - 180'(z - 2) n Ocxi;rlru o n 4 paara menlrprft ni.q p, to 4cx : ll, 4. 360' - 4 . 360' : 180'(z - 2), n - 2:8, n: 1rO. n BiOnoei1t: lO. 34, 3a yuoeoro D : 6 cnr, roAi fi : 3 crvr, Hexafi cropoHa onficaHoro Muoro(yrurrxa o, enucaHoro - b. a) n:3; a=2RJ3, a=6Ja crv.; b=R&, b=3Jd cu;, L = Ba = 18nE cu: pa = gA = 9JE ciu: 6) n: 4; a: D, a: 6 crrr; b = RJr, b =3J, cM; P, : 4a: 24 cNr; P, = 4b = 72yli ev: olo a) n:6; o=o!o R, a=2Js cwib:R,b-gcM; P"= 6a=l2JB ev., ,' Pb: 6b: 18 cu; r n: t2: a =zntsff, a:6tg 15'; b = znsin{fr, b - 6sin 15"; P. : L2a : 72tg 15', Pa: l2b : 72sin 15'. 35. Hexafi pa4iyc onrzcanoro HaBKoJ'ro rcBarqpara i uecrrrcytnrzra KoJra * R. Cropona P 2J = 6 (cru). Toai R = !+, n= * = s.E tcMl.KBaAPara an = Z, an = 4 ,12 lz Cropona [recrr.rxyrHuxa au: R, au: 3rE crr. Pu : 6 ' da, Pa = 18rD (cm). ",=ry, " -g (a€)'J5=2z16 (cm,). Bidnoeido:18uD cm; 27J3 cvt". 36, ,{rs [paBr{JrbHoro rprrr(yrH{r(a gaAaHe rco,'ro e pa4iycom -R e nuucauzu, a Arfi npa- Br4IAEHOtO mecTrrltyTHr4ft a - O[r4CaHrrM. 868 iil: TEOMETPIf, Eeee F. l'1. ra ix. flpoQinrxufi piBeHb iii{i:.:+liii::iiii:*ili 40. Hexait KoopAtrHarrr ro.rxu N(l; y). Tovxa K K(2 =6;l+rl, K( 2: _t). 2 2 ) P * cepe,4una niapigna KN, P( -2 *' :-1*vl, a P(-6: 2t,'oai -21* = -6,rtrl 2 '; o =2' -I + a:4, u:5. or:+ce. N(- 10; 5)' 2" Bidnoai1u: N(-10; 5)" -Ebvb 2 -t;Oi I 2 - iiiai{lt{:iititli;:* rEoMETPle 6ees r. fl. ra ix. Ilp
  8. 8. 41. Hexait roq:ra M(x; O), rcai MO' : (r - 0)' + (0 - O)'z : x2, M P2 : (x - 2)t + (0 - 3F : : x2 - 4x + 4 + I : x2 - 4x * 13. Ocrinrxr.r roqxa M pinuoei4ga,reHa si.q O i P, to MOz: MP2, x2: rc2 - 4x + 13,4x:3, t= +=3,25. Orxe, M(3,25;O. Bidnoaida: (3.25;0). 4 42. Pir;r-ftsss npauoi, flHa rrpoxoAurb vepea 4ai roqrcu A i B: *-l =a-4- x-L=a-4. x l:u_4.x u:_8. -2-t I-4' -3 -3 -- IIs np,nua ni4rzHae ri4 ocefi HoopAuuar npauoxyrunfi LCOD. TTpn r : A -A : -3, y : 3, or:rce, C(0; 3); rpv ll : O r : -3, otrxe, D(-3; 0), ro,qi CO : 3, DO : 3. 11 S,oo= rDO.CO. S^,"" . ;'3 3 4.5 (^".oa.) Bi}noei1t: x ll : -3; 4,5 ",. og. 43. Croponn LABC: AB = JC 4r' - (4 - rf = v6+ 36 = "4f = sr6; AC = ^tE + q" + @ -rf = !66 + e = J+s - z'ls; BC=Jt6-3i +( ,-1)'=Jsl*s=Jeo 3J10. AB : AC, roti LABC - pinxo6e4peHufi. Me4iana, trpoBeAena Ao ocgoBr BC' 6y'4e (a .z -ze t i srcoroio. Hexail cepe4nHa BC - toqxa ,, Ol.t, , Z l. -r{(1,5; b,5), rogi nzcora aa = 1fu - r5y * 1+ - O*ly = 'lt+s. ^ 1-^ -,"=;.sJlo.Jrar=4f ,-""o.,Swc - 2BC All , S*, - t 3Vt0 Vl4.5 - 2- Bibnoeiu: "=t.y *.o. 44. }toop4uHaru cepeahHn.qiarosarir", l+n,+) ' (6:4)' KoopquHarh cepe.{Iu- uu aiarona,ci "o. (ry ru ;'), (6: 4). orxe, aiu"o*uri qorr4phKy.rHItK a ABCD treperr.rnarorbc;r i roqxoro treperuuy 4i:rarsca uanni.n, a orxce' ABCD - rapareJro- rpam.AB={tt-4)'+(1 -6y =,tia, ao=v!t-8,t;G2t =,E6; p=4'126 ot' AB : AD, roti ABCD - Pou6. 3xafi4euo 4iaronari: AC = ^1@ - s!" 41 *y = Js6 * 36 = o"D, BD = Je - 8)" + (6 - 2f = 4Ji. s*"o =! :ic' no, s^"." = 1 alz.ali 24 t^, ot. 2 Bi/noeiu: 4J26 oa.; 24 *". or,. 45. a) Touxu, cnuerpuvni siaHocHo noqarKy noopAhHar' Malorb trporuJrexui xoopau- narz, rouyA'( 3; 5); 6) roqrcz, cumerplruHi ni4nocno oci a6crlui, Marorb nporzJ'rexui op4unatu, ornte, t,(B; S); e) rouu.r, cuuerpnuni uigHocHo oci op4uuar, Marorb npor[Jrerxni a6crlNcu, orxce, A'(-3; -5' Bi1noai1a: a) ( 3; 5); 6) (3; 5); e) ( 3; -5). a7o lilr reouerplg Eess F. rl. ra in. rlpo$inaxnfi piBeHb tlitii{lll::fil*:dl 47. AB(3 -I; 2 - 6), AB(2; - 4); CD(2- 0; - 5 + l), C ru eexropia pisHi. ro AS Ci. 4a. 2d.(2;6), 3i(,6; o), FQ+ 6; 6 - 0), F(s; o); lFl = Bidnoeidu: 10. 49. Bercropn mo,rineapHi, nxuo { = ! , ,*':8. x'- Bidnoaida:x-=!2. 4 2x 5O. Bexropn nepreuArrr(yrrfipui, axrqo 2. x * x (r + x2. + 5x :.0; x{x + 5) : 0, eni4Hrz r : 0 a6o x : -5 Bi1noai}u: r : 0 a6o x : -5. 51. PoausHeNro LMAN i LMBN: MA: MB, AN : B MN - criit:,;.a, orx<e, LMAN : LMBN (sa rprona Hauu), ro4i /AMN: IBMN.. . Posrrr,rueuo LMAB (AM : MB): MO - 6tcexrpuc O -. ' rouxa nepermny AB i MN. y piuno6e4peHoro r HnHa 6icercrpuca, trpoBeAeHa Ao ocHoBn, e Bvcororo MO L AB, MN L AB.IIdo it rpe6a 6yno 4onectz. 52" Hexafty LABC AB: BC, AI< - Bucora, Al{ L BC AC:30 cv, BK : KC:7 : 18, roAi BK - 7x, KC - 1,8x,.4e .r - rcoe(birlienr nponopqifinocti. 3 LABK (ZAKB : 9O") AK2 : AB2 - BK2, AB : 25 AK2 : 625x2 - 49x21 AK2 : 576x2: AK : 24x. i:if:*ii:r..: ]i:.!:.i:.j. 3 LACK (IAKC :9A")ACz: AK2 + KC2,9OO : 57 900r'z :. 9OO, x' : 1,, r - l. Togi BK : 7 clr, KC : 1"8 c*r, AK : 24 cv. s*" =|xc . A.r<, swc =* t" 24 - 276 (cur2); s*, =f,ax.Ar{, s*;-=} z z+= 84 (cu'z). Bidnoei)o: 84 cut2i 216 cnr2, 53. Hexaii y LABC BH L AC, AM : CM, AC : 34 c*r, BH : 24 cm, BM : 25 clr. Posr.r,sneuo LHBM (IBHM :9O"): HM =.t85' 24' = JAs - r4r(rb - 14) = ? (cm); AM = MC - 1.tn = 17 (cm). 2 AII:AM HM,AII:17 - 7:10 (cu); HC: MC 3 LABH (ZAHB:90"): .4-B - Jr4" -iro'= 26 (cm s LBHC (IBHC :90"): BC = .,t876 + 516 = 24nE @ P*" : AB + BC + AC, Pffic - 26 + 24Ji + 34 = 60 54. Hexafi y rpaneqii,4BCD BC : 6 cw i AD : 18 cl O - roqxa nepear,ruy 4iaronaaeft. Pogr.ngseuo LBOC i LDOA: IBOC : ZAOD, ZCBO : IODA, BOOCBC6IToTiABOCNLDOA.::=- ODAOAD183 iitll:iillilllii:i:rt rEoMErPIe 6ees F. fl. ra in. Ilp
  9. 9. Or.nre, 4iaroua;ri tpaneqii nepernrrarorbcg i roqrcoro [eperr,rHy gi.nRrr,cR y ei4no- urenni 1 : 3. Bi0noai}u: L : 3. 55. .{onxcrzna xoJraC : znR. ,{on:rcana a6i.nr,urenoro xona C' : L,2 . 2nR : 2 (L,2R)n. Cropona enracaHoro B rcoro npaBuJrbHoro rplnyrHurca a = RJ}, nJrorqa rpranyrnlrxa ^ o'Ji ,R'8'6S=-':'- =-' :'-. CroponarpaBr,rJrr,Hororpr{Kyrnrrna,Brrucanoroea6iruuene 44 xo.no, a' = r,zR,h, rrrorrla rprr*yrnraxa s'- (r'znv5)" JE =t-148-bF44 L,A4R'z.3J3 , n = = 1,44, sa 44 o/o. R' .3J3 v LABH (1AILB: go") BH =,[+s." -16.'= "J43 Tori sinz =BH "inza-'n6s =@-. ou"--AB'7xL loo sin zABC = sin(180" - ZAI = sin z2! = !2! . ' t;; Orrxe, sin 1A = sin lB = sin ZC = sin ZD = vl" . 7 ,C; 11;7rn6i6n' 1!9. ( 59.' SacroconyeMo reopeMy xocnuycir go LABC: a) 3a nigorrurrz croponarvru. 3 : 5 cvr, BC: 8 crvr i g.er,ao AC. AC2 : AB2 + BC'z - 2AB . BC ' cos lB, A AC' :89 - 40: 49, AC : 7 cltt. 6) 3a ei4olrarzur,r cropoHarrv,AS:6 cu, AC:4cttr _s's'3nafi,qervro nianouennR - : - = ssBi0noei0a: sa 44 oh. 56. Hexafi y MBC (tC : 9O" ZB : 30', AB : L2 cv, B - qenrp xora s pa{iycou fi i n.noula cerropa S"""*. s qerrrpalrbrr,rM nytorvr 30" i pagiycorvr R topinriroe ]S*".3 LABC: BC : AB cos ZB, t: BC = 12cos30" = 12 V: = 6Jd (cu). 2 1 S.^"" =:AB.BCsinlB,2 1- s.,"" = + 12 6Ja . sin Bo" = tgl6 (cM,). 2 =Ir*"= .1. rsJS; @ = sJzt R, -t2'9Js . A AC2 : AB2 + BC2 - 2AB . BC . cos lBi 16 = 36 + B ""' -'*:" + 2o = O; 3Bc2 - 28BC + 60 : 0. Hexair BC- r, roAi 3x2 - 28x+ 60 : 0, *r,, =4 ,, =+= a|, x, = o. Orrxe" BC = 3* c* a6o BC : 6 cu. F; I; Bidnosida: 6^i ovo. i n 57. Hexaft AB - epicr 6arrra, ArB, - apicr 4ou*u, AC - Aonxczna r:iui siA 6arr- xa, ArC, - AoBrrirrHa riHi ei,q AoHbKrr, AC : 3 u, B N ArC: 2,5 rvt, AB : 1,83 ru. ZABC : lAtBlCl, ^ B.r ocxi.nrxn aonr,r 4opinnrororb Ryry HaxrrJry uportenia I |t consiZACB:ZAtCrBt:9O", I I '.oaiMBCNaAlB,cl ,#=#, L .[ACAtCI aei.qxr ,4"8, = *',!"' , 'AC 4p. - L'83| z's = o,6r.z,b = t,b25 (u) : 152,b cm.t Bi1noaiSa: 152,5 cu. 58. Ilexai yrpaneqii.4-BCDAB: CD; BC:AD:3:11. flpone,qeruo BH LAD. e) 3a yuosoro-4C - AB:6 cu, rogi AC: AB * 6 3nafiAeuo,4C ! AB. Ba reopeMoro xocunycin AC2 : (AB + 6)2 : AB2 + 64 - 2AB. 8' cos 120"; , AB2 + I2AB + 36: AB2 + 64 + 8AB; 4AB :28; A coaiAC:7+6:13(cu). r) l{yr /A: 60o rer*urr rportr croponrr BC: 14 Toti BCz : AB2 + ACz - 2AB .AC cos 1A; 196 ro1i,432 - 648 - 160 - 0; AB : 16 c*r a6o AB: - BiDnoaila: a) 7 c*r; 6) 3l con, 6 cnr; a) 13 cu; r) 1 J 6O. Cropucraennocr Sopuy;rarvrn me4ianu, 6icenrpuc fioro croponn a:30 cu, b: 11 cm, c:23 cttr. Megiaua, npoBeAeHa Ao croponr4 ai m' =lQ@' * 4' ^1 =7 1z1tzt+b2g)-900) = 1(ts00 -900) = too; " 4' 4' 6icextprzca, rpoBeAerla Ao cropoHrr a: l! = "*L- @+cr ,, 11.23((11-23)'?-900) 253 256. , _16 F'" (tL + 23)' 34' "I 4 .. Blrcora; npoBeAeua Ao cropour.r a: hi -- ,- p1p - a)( -a' nRz.30" R = o,/gre. l n S""". = 360' :.iil'i:-l:':. ,l+il.iili.i ,flrcrqo r - rcoeipir{enr nponopqifinocri, ro BC - 3x, AD - tLx. Ocrcl.nsr<n s rpanerliro Molr{Ha Bnr,rcaru noJro, to -43 * CD : BC * -4n, orrxe, AB + CD : 14x, AB : 7x. du=M-BC, Arr=tt'."*=n*. A 22 D 872 lii: TEOMETPIS Eees r. n. ra ix. IlpoQinuxur piBeHb *liil{il:llfiilii{l:l i:i:i:ii:i:1:i:i:i;i:i:ii:ii::: FEOMETPI9 Eees f. Il. ra in. Ilp
  10. 10. p - 7 + 23 + 30 = z2; hl = ft ' eua+- 80x64 - tL)ga - %); nl 2, .8, .82^.b5. 4I . h = 9 JOS5.J6 "*.go' 15 '"":"" ""' 61. Hexafi y LABC AB : BC : 6 cm, sin lA: O,4; BH -rrany me4ian, M € BH (BH - nucora i ue4iaHa pinHo- 6e4peuoro LABC). 3a nac,ri4xorr 3 reopeMr4 cnHycia ++ = 2R' ge R paaiyc onncaHoro Rora: sin 14 ,R- 6 =7.5 tcnrl. 0,8 R > BC, rogi qeHrp O onzcaHoro nora .nerrutr sonsi rprrnyrHrrr{a, BO : R : 7,5 cm. Is M,BH (IAHB : 9O") BH ="tZn, - da,, BH -- fibL y = 12 (cu). orxe, pa.qiyc rBlr{caHoro Hora: r -lur, r- 6 2 Ocuil.sxu AII : 9 cIra, ro DH : AD - AE : 24 - I Is LBHD (IBHD: 90'): BD = Jt5' + 72'z = 3'14L noro rpatreqii ABCD, e.pa4iycov ltoJra, otrucaHo o _ AB.BD. AD . 45 no,o lt S*,,= Z AD BH. S*o--:.24 1,2 144 (cu'z). Lb.sJn 24 roai R, Lo'oa!-2 =7,bJ4l (cM). Bidnoaidu: 6 cu; 7,5J41 cv. 65. Ocrcimxz AB : L0 crn, AI( : 2 cw, ro BK : 8 cn ocxi,rrrcu BC : 14 cut, TC :9 cu, ro BT : 5 c*r. s^"".=1BK.BT.sinu,B, 2 1 S.,". . ^ AB.BC.sin/8, 2 za-l ro .L4sinlB, sir*e. l.25 1' roai S,"". : 8 5 :=8 (cu'?). t4 Or:xe, S*r" : Sooc - Soorp S*"" : 20 cm2. Bi}noai]u:2O cv2. 66. V rpaneqil ABCD AB : CD, BC : ll cm, AD : ' BHLAD. att=M.8,9, Alt=21 =11 =s ("* 2' 2 Is IMBH (IAIIB:90') uaemo: AB: 13 cv, AE: BH : 12 ctut.Is LBHD (ZBHD :9O': BO = nEn' * ocnirrxra HD : AD AjI, HD: 16 cu, ro BD = a) Pagiyc -B Hora, ouucaxoro HaBRoro rpaneqii' A onucauoro HaBRoro LAfD (ABCD - piano6e4peua ro.ai R. M- 82-!2. s.^.^ - I AD BH, s^^- ASno"o 2 *" roAi R = l3 20^27 = lo! 1cu.1.'' 4.126 6 Pagiyc r RoJra, Bnr4caHoro B TplnylHlrH ai cropouamu - S a-b+caoo r=i, o" p 2-. 6) V MBC: AB : 13 cn, BC : 11 cu, AC : BD : s*"=.[p@ o)(p' b)(p-, Ae p=t]fff'=22 ro4i S-r" = Jz'L 9. 11. 2 - 7I. 2.3 = 66 (cu'?) i Btrcora,M-rovxanepe- B BH : AB - sinlA, BH : 6 - O,4 : 2,4 (cm). Megiaun rprnyrnr4na nepernHarorb- cs i roqmoo treperlTuy 4i.nnrr,ca y nignorueuHi 2 : 1, paxyroun sia sepuunrz, ro.ai BM ?"n, nl'f =?.r.n= 1.ti (cn). BiacraHs ai4 rovrr neperuHy 4iarona,reir td Ao rleHrpa onrlcaHoro xona MO : OB - BM, MO : 7,5 - 1,6 : 5,9 (clt). Bi}noeiOa: 5,9 cw. 62. V LABC AB : BC, AL - 6icexrpxca, ZA: 2a, ror.'ty ZBAL: ICAL: u, lC :2a. y MBC tB : 780' - 2ZA: t80" 4a. ra LABL Ba reopeMoro czuycie - P+ - = ,N:=," sln ,/RAL sin ,/R' a sin(180" - 4a) _ a sin 4q S]N O( SIN C( Ocniarxil rpr4rcyrnr.rn pisHo6eApeHuii; ro 6icenrpuca nyra C ranox =*# d sin 40 stn c( TeLALC AL - LC . rc= ;no slno-asin4cx =2acos2a. sinlC slnlCAL - sin2o sin2cr To4i BC : a i 2a cos 2s : a(I + 2 cos 2a) i A-B : o.(1 + 2 cos 2c). t,t LABC AC = "c o" sin -B sin -A iel.l.l;!i.l a(1 + 2 cos 2o) Sin 4c = 2a cos2<t(l + 2cos2a). sin 2s Bicerrpucoro nyra B e Brzcora, fipoBe.qena Ao ocuoBu, BH LAC. ls LA-BH BH : AB sin1A, BH : a(! + 2 cos 2oc) sin 2o. Bi)noai4u: cropoHr: 2a cos 2a(7 * 2 cos 2a), a(L t 2 cos 2a), a(7 + 2 cos 2a); 6i- a sin 4C s si;, let ceHTpEcz: s1n cx srn (I 64. Hexafi y aa4anoi rpaneqii AtsCD BC : 6 cu, AD : 24 cm. Mo)fiHa Brncarr,r r{oJlo, ro AB 'l CD : BC },4n : 30 cm. Ocrliarrcu uaeroro rpaneqii uoxrrra onlrcarr.r noJro, ro Aarra tpaneqis pinxo6e4peua, AB : CD: 15 cm. Bucora rpa- neuii AopisHroe Aialrerpy Bnncanoro e sei xora. A flpone4<fuo eucory BH, BH IAD. AH . AD' BC . AH '24-6 =g t".*t. 22 OcHilr,rcrz B Tpaneqrlo B roai ia LABH (1AIIB : 90"): 974 ii:i: reouerprs EeBs r. n. ra iu. npoSinsnufi piBeHb liiilijiililllilt'.:iii: i:ilitiil{,:*:l:l:* TEOMETPI9 Eees f. Il. ra in. l-l
  11. 11. B) yAAcr: cD:LBcl*,AC:20cm,AD:2:_ew,togi p= 1'3+29+2L =27 (cv, S*,,=,lir.A 7-=3.7.6-126 {cn2); r =!#-+f,rca. Bidnoaidu: ar I0l cu;6) 3 crvr: nr +f crr,. 68. Hexafi cni.nrna xop,qa.4B HiJr ia eiAnoni.qEo qenrpoM Or i pagiycou r ra qenrpoM To.4i Aiarrnerp naft6i.nrtroro Hpyra D : d', I d'" t t, c -n(d!+ d)2 -( y: -4J = I td? +2d.d^+a! -- 4 4 4) 4-L --'-z LADC - npauoxyrnufi ia npamum xyrou ,4, *cr AH - rln.cora npfiMonyrHoro rprrnyrHrrrca, onytq :HD cH, AH=#, ;ur=t, li)'=a,a". Orxe, nnoula S BanrplrxoaaHoi (pirypr,r: " =; l;' 3r6ro"r6o,t 4. 8 73. ItoopAlrqari(x;ilrorrrcu,r{oecepeArrHobni4pie o6.rrzc.nroemo Ba SopMy,'iaMfl : ^- xrtt, _._attUz 2"2 Ocxi,'rrxu I((1; -1) - cepeAr,rua ni4piaxa BC, p,e B(-2;1), ro 1 =-3:t' aai4xr'r x': 4; -1=+, sni4xn y : lr, uc(4; s). .L - cepe4rzna AC,ro4i t=-3ia =0,s, ,/ = -!-3 = -2. o.n.e, L(o,6; -z). "2 O, i pa4iycolrr R; ZBOA:124", ZBOA:60"' Togi AABOT, ge BOr: AOr: p, pienoctoponuiii, ocxi.nrxu IBOA: ZBAO2 : /ABO, : 60'. Y LO'BA: BO1: AO1: r, BA: R, IBOA:72O", rogi IO,BA: IO.AB : 30". Sareopervrorocu'ycie . * = o'B sin ZBO.A sin IO.AB' RTRTRG "*120"=sin3o" =T' ;=uo' 22 2 Bilnaeila: J3 1. 69, 3a uar. 33 niApy.rnura rcBaApar yntrcaHo B IcoJIo' rra cropoHax r{BaApara s}c Ha 4iauerpax no6ygorani nirxora. Hexafi cropona HBa,qpara.r, ro4i fioro 4iaroua.nr', sxa e AiarrerpoM orrilcauoro KoJra, - "Ji, Tlnot4u KraApara S*". : t2, trJlorqa orrrr- nr12 nx' 2 fix' canoroKpyra- S*0.= ti , ".".=T =f. Cvuan,rol1cerueurie,,sxieir- rrrHarorr,c,s niA rcpyra cropoHaMrr KBa,4para, S*",. : S*. - s.", S""." = :L - x2. Cyua n,roq nicnpyriB, no6y,4oaauux Ha cropouax xea,4para, Aopinnroe 25 = 2 4 = ilx' ^ nx' lllx2 ,l rtx' Tx' =:. Cyuan,'rorqcepnuxia S.*"' 2 -l Z -*')= 2 - 2 n*'. Orxe, S""n". : S*,. : 12, nrorqa cepnuxir 4opienrce n.nouli xra4pata, llo ii rpe6a 5y,ro 4onecru. 70. @irypa, Bo6paxceHa Ha MaJr. 34, cx,ra4aerr,cs B np,ffMoxyrxur{a 3 poauipauu a i 2a ltrJrorqerc 2a2 ra ninxpyra s pa4iycom a i n.norqero S. nnoulu 6iryp _-.2 Sa = 2a2 + "* . IIo6 orpuMarl4 Barflrpr.rxoBaHy Sirypy, rpe6a nupiaarr ia aaaairoi I _-2 Ta' girypr 2 unepri Hpyna a pagiyconz i nrorqero 2.i-xa'= -11. Ilton{a Barrrrpr'l- " fia' na' xoeaHoitPirypu S=2a"+ : - = =2a'. Bi}noei1o:2a2. 22 71, 3a ivra.r, 35 ni4pyuurxa MaeMo: n,'roqa S aanrtpu- xoeaRor ipirypz gopinroe pianuqi n;rorqi Sr. xpyra s safi6immiaM giamerpou ra cyMt4 Sz + SB 4rox in- urux xpyrie: S: Sr - (S1 + Sr). Xopga.4ll, ilIo rpo- xoAr4Tr, qepes roury 11 AoTr{}ty ABox meuuux rpyrir, gopinnroe a i nepnengnryJrspna 4ialvrerpy CD safi- 6i.nrnoro xpyra. Hexait AiaMerp oAnoro B Merlurux -)2 -/2 xovrin d, i S. - 11. a rDvroro - d" i s" = 1:? . 4''4 Bi}noei.Oa: (O,5; -2). 77. [,tts xea4para ABCD ni4pieon AC - 4iaronaar'. H ronareft. ocri.nr xuA(2;*5),C(2:-tl,ro xl?!3t =#K(2 ; -B).,{i a rona,ri KBa,iIpara BaacMHo nepneu4nry i 4i;rerrca ror{Koro K napni.n, AoBrnr,rua no.nonzura na.ni 4opienroe 2. ToAi xoop,4uuarr{ Beprflugr. B(0 Beprrrlrrt4 D(4; -3. V rra4pari Torr(a treperllny 4ia .reii e qeurpou Btrucauoro ft onucanoro ri.n. Ilenrp caHoro norra K(2; -3, pa,4iyc fi : 2, ro/-i pinnarna caHoro Korra (x - 2)'+ (u + 3)':4. Pagiyc nnrcanoro r{oJra gopinnroe no.nonragi cropoH nBaApara /3 = V'(2 0f + (-5 + sf = 2ii, rofi p otr*re, pieHatn.fi Blrrcanoro xo.na (* 2)" + (a + 3 Bilnoailu: or{cane xo.no: (.r - 2)'. + (a + 8)'z : 4; Brrr4caue Ho;ro: (.r - 2)" + (U + 3)2 : 2. 78, Pinn,nnnsogHororcoJra: tc2 +A2 - 4x+29:O;x2 - (x - 2' + (y + l)': 5, fioro qeHrp (2; -1). Pinnnnua4pyroroKorra: 12 +y2 + 4x*6y:3; x2 *4 (r + 2)2 + (A - 3": 16, ftoro qenrp (-2; 3). Ilp.fiMa,.ffKarpoxoAr4rr,arepe3rourv (2;-1)ta(-2;3),u x-2 u+I x-2 u-l ^orfir€,4-t ., - --! 'i2 x-q+l:x-"'--'-2-2 3+1' -4 4 BiOnoai0u:)c+V:L. [i{:il:i{r,{ii{iii;$i: TEOMETPI9 Eees l. fl. ra ix. Ilp .,;rt.!.1:._' az6 li:;: rEoMETPlg Eess F. t-1. ra ix. IlpoSinrnut piBeHb lJJilt::ltlit:t:l:ift
  12. 12. 87. J{nrqo m = d + 26, ro lfil= Jrn' = J@. r6f ='td 4d6 + 46' = = 'rE + 4di | + r" - .tTa-b - 8. Crarapnzfi 4o6yror a5 -lal.l6lcos4a,6l, au - 2 1 cos60" = 1. roni lrzrl =J+*e-zG. Bidnoaia: 2J3. 88. Poeussevo s LABC reHropu -4-B i Au. Ac =lAul lAcl.cos.1A, AB. AC zsitltu cos/A I'qnl lac AB(4; 3), AC(3; -3), to4i AB. AC = 4'3 +3'(-3) = 3; @E1= "@ +s' = s, Acl = vEL (-sf = SuE. orxe. "o" zt = --j-^ :?5 3J2 10 -t; Bidnoeida: Y. 10 89. flxqo xyr ryuufi, ro siu Harexzrr II roopgrnarniit usepri, a Kocuuycu'ltyriB Ilvsepri ua6ysarorr,ei4'emHux3HaqeHb. "o"o-,,2 b,'. ,n t0, lb >0: cos o o, nxulo m .b < o: lml bl nL.b =6.(-5)+a(a 1)- -30 +a'-a, a' a - 30 < 0, nopeni rpuureHa ar: 6, u^ - -5-'l Ilpouinrnn straxocra.nocri: ---1;--'t--i a e ( 5;6). ,flxrqo a e (-5;6), ro cr tynufi Hyr. . Bidnoaidu: ae( 5;6). 9O. 3a ymonoro BeKroph 5(i - 4b i d - 2b nepneHgnxylapni. a orxie, ix ctcaaapuuil go6yrox4opinHroeHyrro, a caMe: (54= -4txo 2tt1-O, 5a'-nab;4oi +862 =O; ypaxoByroqu, ,qo ]al = 1, d2 =!, Ul=t, U" = 1, uaemo: lkdb =13, aa :11. g*rqo 13 14 xyr mirr a i b -o, ro coscx o, f-, "o"o = .'o- -!t.lal lal 1 .1 L4 Bidnoeidu: E, 14 93. Hexafi HoopAuHartr BepurHu O Aiarparrarz BopoHoro O(x; U, rovrca O, - roqna nepernuy pe6pa OM a AB, Ot(2; 4); M rouHa O, roqKa neperrrny pe6pa OK a AC, Or(0; 0); rovHa O, roqxa neperrHy pe6pa ON s BC, Or(3; 1). 3Hafiaemo KoopAilHarh nepneHAnHyJrffpHlrx sercropie: I ) OQtx - 2: s - 41. enrc: zl: Oq an - O. 6(1 2)+2(y-4):O;3x 6+y 4:0;3x+ g :10; 2) oo,(x - o; a - o), oS@: y1: cd(-z: q: oq cn - o, -2x + 69: O; x + 3y: O; S) OO"(x-3;a-1); C,e(+; S): OA" CB=0,4(x-3)+8(y 1):0; ')c-3+2a-2:O;x+2y:5. 878 :::;i: FEOMETPIS Eees F. Il. ra ix. l-lpoQinuxufi piBeHb :iiiiiiiiiiiiiii::ii:i;i:i Poas'srxeivro,czcreuy pinnaHr,: lxt2s=5, )x+2y=5. lx+2u--5, lx=3. I xtss=0: l5y=5: Ia L [y=1. Itoopgunarz rouxu O(3; 1) - rouxa Or. Piessxss oM a6ooo,, * -3 =g -I. * 3 .a - ' 2-3 4 l 3 3r-9- A-1:3x g-8. --3_g-l. x-3_APisHsHHsOKa6oOO,:l x_}u_O. '0 3 o-I' -3 -l SHaiisenrro axy-ue6y4s rouny X na ON: X(m; a), ro +(z +3)2, XBI:(m 5)2 +(n-5)2,ornce,(m 7) nlz 2m i I + n2 + 6n * 9: m2 -lom + 25* Hanpurc;ra4, m : I, n : 2 i X(1; 2 uatetxurt ON ro4ipinnrnna oN a6oox: # =T: *-,-L- t t,,:a -v Bidnoei}a: (3; 1); 3r - a : 8t x - 3a : O; x + 2y : Po3.qln il. BCTvn AO CTEPE AC: ix cxa,rnpHrfi ao6ytox A(-L;2 ,:{i.Li:.i B(5;5 1 14. a) 1) AD; 2) AA,; 3) CC,; 6) 1)A e (A4B), A e (A.BC), A e (AA'D,); 2) C, e (CrCD), C, e (BtCtDt), C, e (C'B'B); 3) D e (ADC), D e (DD,C,), D e (ADD). n) 1) B, e (ABC); 2 B, e (BB'C'); 3) B' e (A$tC) 115. a)AB; 6) B e (ADC); e) AC c (ADC, AC c (AB 117. 1 18. .t'/ /t"/ ryp/ l2O.,flHuro4sinrorqununapalersHimimco6oro,ToBo qacrrrru. .fnrqo 4ei uoilIfiHtr treper[Halorscs, To Tlrpn llacTuHv. l{i:ifii;tidiiii.;i TEOMETPI9 Eees F. Il. ra ix. rlp B{3;5) S 3. OcHoeHi noHcrre crepeoMerptt- OcHossi $irypra crepeomerpii: rovra, fipsMa, rlJaonl fIoanaqeHH,f : Toqxui A, B, C, ... flprmi: -4-B, AC, BC, ... a6o a, b, c,... flnorquHu; (ABC), ... a6o a, B, y, ... flpnua.n6rxnicrb roqru 4anifi upamifi: A e a. Heupuuarer+cnicrr, roqxu ganifi npauifi: B e b. flpuna,rerxnicrs npruoi 4axiii rronluni: a c a. Heuprzna.ne*cnicrr npauoi ganiit n.norqzui: b cl 9. fleperzH npsMux a i b s ro-rqi C: a n b : C. Ileperuu npanroi a i n,ronlaHu o e rovqiA: a ^ cx Ileperuu trrorqr.ru n i B no npsuifi c: u n B : c. o(x;y)
  13. 13. 125. flxuope6pory6a a,V:43:8 cm3, rogia:2 clrn' S""".:642, rogi S : 6 . 4: 24 (cv2), Bi)noai)b: 24 cM2. $ 4. Axciorvrn crepeoMerpiiixacni4Ktt s xtax Cracrelira arciom crepeouerpii cx.na4aerbc,s a axciolt n,raniuerpii ft aHciouu npz- naaerxHocri roqor i rrJlou{vH, axcioun neperrHy nJrouII4H ra axciovn nr'loruuHu, .fiHa rrpoxo4r4Tb vepea 4ni np,sui, uo neper;4rarorbcfl. Ancioua [pfirtaJreilcuocri ro'rorc i nnouluu. ,flxa 6 ne 6y.na n.norqana, icuyrom Toqnu, rqo HaJrer(arb qifi n.norquui, i To'rnrl, rqo ifi ne HaJrerfiarb. Ancioua neper{Hy nnorqun.,flxr4o 4xi pisni nJronlunri :uarorr, cni.rrruy roqny' ro Borrn neperr.rHarorr'cs IIo npnuifi, nlo [poxoAr,rrb qepeS ilro rotlKy, Arcciorra lJrorquur{, sfta npoxo4urL uepea,qni npgrui, rqo neperrrfiarorbca. ,frqo 4ni piani uparvri marorr' cni.nrry roqrty, To qepeg Er,rx Mo?r(Ha npoBecr[ nJIorqflsy' i 4o roro x ri.ntxa o4ny. 3a nac.ni4xallru a a(cio1u crepeonrerpii, e4vuu:ol rIrrHoM npoBecrr{ nJlorqr'ruy MolfiHa: l)uepea npauy i rorrxy, rqo rre Jrexcllrb na qifi npgmift; 2).repes rpr.r roqxr,r, qo He Jrexiarr' Ha o4nifi npnmifi. ff&qo,qei pieHi rouxu nparvroi naaexarr n.nouluai, To np,rMa' rqo flpoxoAr{Tb qe- pea qi rourra, Jrelfirrrb y 4ifi n.norqzni, Ilaorqltra poa6uaae npocrip na 4aa ninnpocroplr. ,flxrqo roqrcrz A i B na.lexarr oAHoMy ninnpocropy, ro siApisox AB rre fleperrrHae nJrolqrlHy. flxqo rouxu A i B Harer{darb pieuuu ninnpocropaM, ro nigpieon -4,8 treperrrHae nrolqr'ruy. ,{.nr 6ygr-rxux rouox A, B i C npoctopy Br'rnoHyerbcr nepinuicrr rprrrcyrnrrna: AC<AB+BC. 1 42. rlepea Asi Aani piani ro.rrtr Mo?rcHa [poBecrrz np€My i rinrxra o4iry. rlepee npauy Mo)rcua npoBecrx 6eaJri.r nJIotrIuH. 144, flpwrrycudMo, rqo rosxa M - cepeAr,rna siApisra.A.B -. ila.nerxlrrr c. Ocxi.nrxr'r A e a, M e a, ro npav'a AM c o aa axciorvroro Cr, a orrxe, aigpieorc -43' qo Jretfirrrl na npalrifi AM, new-:rrrr y flrorqaui cr,, roqrca B e cL Iqo ue ei4noni4ae yrtori ea4a- .ri.Orxe,Mes, Bi 0n oei0a: He HaJren(ilrb. 145. Ocrinrxu B e a, Toqepea 4 i B MorrcHa npoBecrr4 rlJlorqrrHy o, i rilSxrl ogxy (ea nacnigxou a anciorvr crepeonrerpii). Orxce, B e a., a r_o. ToAi Bci npaui, r4o npoxo- AfiTb rrepea rouxy B i neperunarorr trpflMy 4, Marorr' 3 nJrolquHoro oc no 2 cni.nrnr'rx rouxra (r. B i rovHy npnuoiA), rogi aa arcciouoro C, rcorxna s Irr{x fip,ffMllx Jrexcr4rb y urorquni cr. IIdo fi rpe6a 6y.no AoBecrrr. 146- Hexaii y rpaneqiiABCD rouxnA, B iO - rotrfta rtepertrHy 4iaroHa-lefi Harexcarb nlonlr.rni cx. ToAi aa axciorrolo C, npnui AO i BO Jre]$arb y n.riorqnni n. Ocxi.nr'xra ro'rxa C e AO, ro C e cr; ocxirsxu rorrxa D e BO, ro D e o. 148, Ae a, BM c cx, To.rxr.rA iM sanetxarru,roniAM ca i ro.rxa C e AM, C e c, To.rxu Ai B na.rexatb o, roAi AB ca. ToqrcaNe ,4-8, roaiNe cr. Toqr<rz CiN sare- rrcarb 0(, orraie, Ba axciouoro C, aucora CN na.nerxurr cr. 149. Hexaft tpu rovxra A, B i C ,rexarr y r;rotquni o. I]i rou- Krl e BeprnrruaMu LA-BC. Ba axciouoro C"AB c a, BC c cx, AC c c. Ornte, no:nua ro'Jrca A.ABC Jre)fitrrb y n.noiqnui a. 150. Hi, He Br{rrJrrrBae. HaflpuxraA, rprr roqxr cropoHr{ AB rprzxyruura ABC uate- ?*carb,nrorquHi c, a rourca c e o, 880 {::i: rEoMETPlg Eees F. Il. ra ix. IlpoQinuxufi piBeHb;i{iiia:::ii::*!li;iii 1 5 1 . 3a uac.niqxopr a axciou crepeome'lpii, vepec 4ni np Ha rrpoBecrr?r ilJrorqrrHy i rr.rme oAHy. Hexaft MA MB c a, By4r,-srci npcmi, rqo neperr,ruarorr MA i MB Epoxo,4fiTb qepea Toqry M, lratorr B nJrotqt4lrorc c 2 Torrnrr, a orrrce, Ba axcioMoro Cr, aerxarr y n.norqr.tri o ft rpeda 6yro 4onecra. r{epee rouxy M morxna flpoBecrr,r np,fiMy, sra r{ nit4Tb y n;rorluni o, a neperaxae ii lurrre n o4nifi M (nanpr.rrrag, upaua c). 152. flparri-4Il iAK neperrnarorbcff, orsr{e, qepeo Hr{x fiKa neperrnaerbcfi B nJrorqlrHoro cr rro npsuift BC. 3a orxe, P e B. Tourca K e AC,K e B, To,qi npnua KP .I(, ro6ro Mae B nJrorr{rruoro B .nrrre o4uy cni.nrny ror ,43. Orxe, npaua KP He rreperr{Haerrca a nparvroo /- 154. Ilpana BK neperrnae rrrrorqfifiy (AAp) n rovqi K urorqrzHy (ABC) n ro.rqi B. Ilpaua BK fiepervnae nJr (ArBP). Ilpavra CK reperurrae nrrorquny (A4B) n rovqi,K, nrrorqr,rHy (,48C) n touqi C, n,roqrany (BCC n rovqi C, Ilpama CK uepeurnae rrrotqrrHy (ArBrCr). 155. Ocri.urxu npnmi a, b i c.nencam y n.norqzni oc, a r rpsMr4x,rode o, Beo',C e cr.SayMoBoro/.e B Torrnlr ABox rrJrorr{aH Jrerr(arb ua npatrift neperr4Hy q B i C.nqnrarr na ognifi npanift. IIfo fi rpe6a 6yxo 4o 156. Ocxi,rsxu nJrorqtur4 cr i B neperrzrarorbcff rro npau yci cni;rrui Torrxrr rrJrotqlzu. Ilpaua D, arca .nexrarr y o cni,rrny roury K. To,qi K e a. ll{o ri rpe6a 6y.no ,4o 157. a) Ilparvra DrK.nexnrr y nnorquni (lArDr), nxa nepernrraerr,cfi B nrolp,rnoro (:4BC) no npanaift DA. To4i cniarna ro.nca npauoi.QrK i n.norqunn (,4-BC) Cl Jrex{rzrb na np,anniii DA. N - rovrca neperrruy np,fi- mux DrK i DA, a orlr{e, fipaMa DrK neperrar:ae nrrou{rny (ABC s ro.rqi N. 6) flparraa BK ,rerxam y nnorqlrHi (AArBr), at+a rreperzrraerbc;r B [ro]qr,(Horo (ALBP) no npavrifi BrAr. To4i cni;rrna rouxa nparroi BK i n.norqrzura (APP) rrelr(arb na nparrift BAr. M - roqr{a re- peruny npsuoi BK a n;rorqranob (A'B1Cr). 158. a) Ilpnni MN i ArBr re)r(arb n o4nift n.norqr,rni, ro,qi -O - ro.rxa ix neperrrny. 6) Il;rorquna {B$C) i rrlroqlrHa (A,B,C'), axa micrr,rrr npamy MN, neperffHaorbcs no npamift CrBr, Togi rovHa neperr4rry npfirroi MN i trJrorqraurr (B'BC) nexurr na npaivrift CrBr, rour.ca F - rorrna ix neperrany, e) CiuHa naorqr.rua neperlrxa€ ocnoayArBrCrD, no ni4pislcy M.|y', n.norqrany (BBrAr) no nparvrift ,EB, a rpaub BBTATA * no ni4pisny PB; n,rorqzny (BBP) * no nprnrifi BF, a rpanr BBTCTC - no N A :iiii::iiiiiiii:iiii rEoMETPlc 6ees r. It. ra ix. Ilpoe
  14. 14. BiApigrcy -RB; rogi ryaus DDTATA - no ni4pisny MP; rpaxs CC.DtD - no ni4piexy N-R. fl'aruxytsux RNMPB - nepepia rcy6a nrorqzuofi (NMB)' lllrouqnua (BBp) treperrruae nparvry MN y roqrli K" Dl llepepia RNMPB i nlouqzua (BBp) rvrarorr 4ni cnimni N 174, Cissa nJrorqrrna Mae s trJrorJnHon (ADC) 2 cnilrs KC; a n.norqranoro (ADB) - roqxlz K i B, a orxe, npa B nroqzHaMr {ABC) i (BCD) - roqt<n C i B, a ornre BC. Ilepepiaou e LKBC. 175. flrcrqo civua naorqrzna [poxoAr4Tb qepea nprivry,43 t<u A i B Halexars ciuuifi nrorquHi. Ocxi,rrxu ciuHa Ha lpoxo.4r.rTb vepes rovru i4 i M, ro AM - cni,rrua civnor n.norqrzHz i nrorqunr.r (ADC'1, aua'lorivno, ciun rquna i nnorquna (BDC) lrarorr, cnimuy nparty BM [Jrorr]r4Ha neperuHae rrJrorr{r4 Hrr (A-BC) r (BAD no npam Ortxe, A,BMA - uryHanzfi nepepia. 176. 1 7 7 . a) Ciuna n roquHa neperrrnae rp ans D D rC rC no ni4p PT; rpanr BBTCTC no nigpiary -KP; naorqlrny (-A-BC) n r S, S e I{P, S e BC ra no upamifi S?. Sf treperrxae e rourli M. V ci.rnoi trrorluHu i rpani AATBTB 2 cni ro.rnrz Ki Mi ni4piaox KMi y ciuaoi n.norqraHt irp ABCD - ni4pisox MT. Orrlrc, myxauuii nepepia - q prxyrHrrft MKPT. .. 6) Hexafi aa4aua nipauigaABCD. CropoHz nepepiey -i ?I{. Ciqsa nrorrlnHa nepernHae pe6po CD n rovqi S r4nny (BCD) no nprmifi SP, arca nepertluae BC n N; rpanr ABC - ro nigpiany KN. To4i qorr.rpr.rxy KTPN - uyranufi nepepia. e)Dr) 180, Terpae4p ABCS -npanunr,nlrfi, ycipe6pasnoro4 peguHu pe6ep S.4, SC, SB, ro4i uyxanzvr nepepiaou e L Ocxi,rrnu rouHu K, M, N - cepeAr.rnu pe6ep, ro KN KM - cepepai .niHii ni4noni4no rpuxyrnrzxis AASC, AABS. ^ KM,Js li)' It o,JB 5rrr=-4 4 = 16. Binnoaint: +t + iil:ji;:li:ii{::r{::* TEOMETPIC Eees f. Il. ra in. IlpoQ M roqnv B i K, roai KB - nisis fleperuHy n,rorlux (MNB) C, i (BB1D1). r) flrorqrzna MND neperuuae rpaHtAlBrCrDr no nigpiany MN, rpaas AATDTD - no ni4piaHy MD, orxe, linia nepe- rtrHy nrrorrluH (MND) i (A D) - MD. 159, a)MN iAC .nerxarr y n.norquHi ADC i neperunarorlcR n rouqi K. 6) Ilpaua MP tetxvrr' y n;rorqrtiri (ADB)' axa neperr- Haerbcfi s trro[{r{Holo (ABC} to npsuift,4B, or]{ce' roqxa S neperuuy MP i nlot4unu (ABC) newurr na AB. n) flpaua NP ,rexurs y uorilnui (BDC' axa treperr- Haerbcs B rrJrotr{r.Inoro (ABC) no nprnniii BC, o'nxe, rouxa T neperrany NP i nlorqxHu (ABC) textwrr na BC. r) Il.norqzxn (MNP) i (ADB) narorr 2 cninrsi roqrtn M i P. rofi MP linia neperuHy rlrx n,'rotltrH. 16O, flxrqo MN ll AC, ro flpsMa MN i n,'roulzua (A-BC) He neperxHarorbcfl. '162. Hexafi aa4ani npami ai b, npava a Jlextzrb y uorquni 0(' trpfiMa b nepetnuae qro trJrorqrHy e rouqi A, A e a. Hepes trpfiMy 4 trpo- BeAeHo rrr'rou1hHy o, flKa fleperilHac npRvy e toutli A. gepee npsrry b trpoBeAeMo rrJroflIuHy 0, sna uepe- rnHae [psMy a e rouqi B. To4i nJrorrlrHrt cr i B ue- perzuarorbcfl rio npauifi AB. Toli n.lrotql,rntr c[ i p treperrrnarorbcs no npamift,4-8. To.{xaA € b, B e a, togi upama l-B treperuHae i a, i b. 166, Hexait y ny6a ABCDA.B.CrDl giaroHarr CrD rpani DDPTC gopinuoe: C1D : d, rogi pe6po xy6a cropona RBanDara DC = L. ,lz .l O6'ev xy6a V DCr, V -' d ;"0;,,"",;:' ft -l'Dr $ 5. flepepisn d" 2J2 clB Toni KM NM ' KM =f,,, ,"u, ".;=+, IIpu no6y4oni nepepisie Br{Rop14croByeMo naacrusicrr: flrrilIo AB1 rrJrorr{uHr4 Ma- rcrs 2 piaHi cniasni roqxu, ro ui nnorqnHu nepertrHarorbcfl no npnuiii. ur,o npo- xoAr,{Tb qepea qi rounu. 1 73, a) Ciuua nJrorqtrna Mae 3 fiJrorrlnHow (AtB rD t) 2 cnrnr'nr rouru B, i Dr, to4i ix cli,rr,sa npRma B,Dr; y civHoi n;ro- Ar quuu i tr,rolr{uHu (AAPJ - npsua A-Br; y ci.unoi trJror{u- Hu i n.nonlnnu (AAp) npsrra.4,Dr. To4i myxanufi ne- pepia - LABID 6) Hexafi cepeAurra pe6pa DDr - ror{fta M. Ci'tHa trroqrr- Ha, nro npoxoAurb qepea rout<u A, C i M, neperunae rpaHb A AAtDlD no ni4piexy.4M; rpant' DDTCTC - no siApiexy CM; rpausABCD - no ni4piaxyAC. Orme, uryxauur? nepepia - LAMC. AA2 ::::::: fEOMETPIg Eees f. Il. ra ix' l'lpo$inuaui piBeHb:i:i:i:i:1:i:i:i:i:i:;:i:!:i:i:;:i
  15. 15. 181 . Hexai y rpsMonyrHoMy napa;re;reninegi ABCDATBTCIDI AD :6 cwr, DC : 6 cu, DDt:8cluiM - cepe4unaAD, T -cepegnnaDC,K * 81 cr cepe4rzna DD,. Illyxaxra* nepepis - LMKT. MT - cepeA- ns ninis LACD - npfiMonyrrroro rpr'rryrHlaxa 3 lcareraMu 6crvri6cu; AC=6J2 cu, ropi MT=1'u"1,=aJZ (cru). '' 2 MK - cepe1:r..a ;rini,n LAD.D - np,fiMoxyrrloro 3 Karera- rvrz 6 cm i 8 cu;.ADr : 10 crvr, roti MK=1 16= 5 1"*;' KT: MK. v ^MKr o=Mx+t{+mr =4#=L5vE+5. S*"r=@, = J1s * r,sJz). r,s,D.. t,rJi. (s - r,sJz) = = L,lJt. J% - r,r*, = L,sE'E = r,sJm rc*t' Bilnoeila:1,5Jfi cu'. 182, Illyxauufi nepepia xy6a ABCDATBTCTD, - MB:C - pinnocroponnift, ocKi'nr'ltr'r #;.Ur" = AC = aJ2 - giarona;ri nna4parie ei cropo- orl,ce, P14s =zali. ,*"=# - (o'li)'Js o'JB b*s=-T= 2 . Binoeidu: ,"A, #. 183. IIIyHanufi nepePis - LMNC1. MN - cepeAn s ni:rrir LBCD, ge BD = alt, ,osi MI'{ = $. Ie ANC'C (lCrCN :90"): 41 K A _"Ji .a 448 I 88.Cnig nroqranz nepepiay:. - na rpani - ArDtD - KDi - Ha rpaui DDCp * DrP; - na n"noutrrani nrzrrtnroi rpani .- r. X i r. Y i npaua XY, sua [eperr{Hae ,48 n r:ouqi S, BC - e rovqi I{S, na rpaai BBpp * TP. ToAi uryxanufi nepepis - n'arrxyruax KDTPTS" Clqnoro nrorqnHorc BaAaHoro reapaeApa (napa.ne.nenine no o6u4na 6oxra ni4.aroi e roqrr BaAatoro rerpaeApa rrJror{r4Ha neperuHae rparii rerpae4pa (napa,re.nenineA rcyrrrrrx, cropoHaMn fiKoro e qi nigpisnu, HaauBarorr n pa.neaeninega). ,{:ra no6y4onr nepepiain,qocrarnr,o no6 civHoi n.rorqrauu a pe6pannu 'rerpaeApa (napa:re.renine xorxui 4ni no6y4oaani To1rrcr4, rqo reJfiarb n o4Hifi rpau Ocrcinrnlr rerpaeAp wrae 4 rpani, ro fioro nepepiaauu M a6o vorapuryrHurcu. Ocxi.nstu napa.ne.nenine4 mae 6 rpanefi, ro fioro nepep r(yrHrrxrr, rlorr,IpurtyrnlllcH, n',*lturtyltxz(8, mecrlrxyrn 194. Illyrcanuii nepepio - MDM. flxuqo DA: DB : DC : 5 crv- AB : BC : AC : ro MaeMo: AM - nucorya piunocroponnroro AABC ACh 6.,5 -AM= 2 , or*te, AM= 2 = 3V3 (eM). crB1 Ar V piano6egpenoro ACDB DM - eueora i ue4iana ^^CDM - npauonytnlrft, Clt =nC = 3 cm. 2 la LCDM (ZCMD : 9O"): DM : 4 cyt. P*o, = 5+4+ lliiL..--...-. ';:t{.:i.:.:.:{'i!. C1N : MCy llinnepuuerP LMNCT: t( ali "'6) o'[i "JiP=rz*''r,=4+2' _ ro4is-u.' =iit ,.2,1 [ 4*z-2)l 4n2-2]= G$ '$,("i a'[zt(alr'z =ll a * z t z - 4 ) 4 )= 884 l{i;i rEoMETPlg Eees r. rl. ra in. l'lpoQinunrr piBeHb tli:iirdil:il:**;'-:i': p = 4,5 + 5uE cu. S-.= =v o =@=t,b.,69 (cm'?). BiOnoeiu: g+3rE cnr; 1,5169 cu'z. 195. IIIyxaNzft nepepia - MMC, y slcoro AM : CM, A Posussemo LCMB: lB: 60o, ocrci.nsnu LCDB - pin poniriii, CB : a, *U = t. 3a reopeuon xocunycie CM' : MB2 1- BC2 - 2MB . B CM2 =a2,o' -2.a.g=a, *t--4=a, -U' =79693993 itiiji{iri;:iit::{iti TEOMETPI9 Eeee F. fl. ra ix. IlpoQ *" =t, CrC : a, rogi CrN =
  16. 16. 197. C:ria trJrorr{rHr4 fiepepisy na nparvriii -43 - roqna X, na npruifi BC - roqxa Y, 199. Ciqsa nJrorqlrna neperrrHae nJron{rHy (AAB) no n nJrorqr.rHy (CC$) - no npanifi BrC. Idi nprui neperunarom ArBr - y r:o.rqi M, BrC, y rouqi N. IJJyxawir repepia - rpareqiaAMNC. 2OO. Ciqsa r.noqrirHa fieperrHae ntorqrany (-4ArBr1 no np AB", axa [eperrrHae ArB, e'rouqi M; trJrorqrruy (BBp) - no npavifi B"Cr, axa treperr B,C, y rovrli Cr. C,riA ci.lnoi nJrorqrrur{ Ha n.lor (ABC) - roqnu A i Cr, orxe, npav'a AC2, srca fiepe DC e rovqi N. To4i uoraprnyrnunAMC.N - nynaxzii nepepis. Oc o,li "h t zJt a oJ7 To4i P-.n,=a+2'l = g (cM).P=2* B ffi,J, oJit' f'tT 'le, "A's*-'=/lt.- Jti' t -o)z*n - s, ) !l; *zlt s -tl r) - a 2 altg _o'Jts 612 o" JLg cM: - L2 (c.'). cu2.Bionoeiov: "6 * z"li) 3 ua n.norqzni (13C) nparra XY. 3a yuonoro 1 1119 -'- BB,, NC ll BB,, orxe, NC - cepeAHs 2- rinia ABBTY, ro4i C - cepeAr4r{a BY. Asalo- riqno A - cepe,4uaa BX, or:ne, npaua XY npo- xoA[Tb qepeo rovxy D. Yotzpurytnux MBrND - uryrcauuft nepepis, HolKBa cropoHa fiKoro c rinoreuyaoro npamo- Kyr'oro rpurdyrnrrxa B RareraM[ a i 9, orxe, MB.ND - pou6. B cr guaa BB", ro MB, - cepeAu,ff ninin MBB, i Arra.noriqnoN - cepe4unaDC. V voruprarcyn- nuxaAMC,N yci cropoHu c rinorewyaa:vru pis- Hhx npsMonyrHr.{x rpriKyrHr,rHis o Hareral{u a i l, roAi AMCTN - pom6 ai cropouoro 2 E 4!D 2 mn,- f t,r' !""*lzJ ls LDNC (,/DCN 90') ,N = Fe t- t- . dvD avc , roAi Pr",n, = 4' Z = Z 3Hafi4emo 4iaroHa;ri pom6a MBTND: MN = AC = axii; giarona.nr BtD ny6a: BrD2 : 3a2. BrD = aJT. s"qno = )u,o **, s,^nn L, "A "Js="'!9. E A./b 2 P*","=+ f =2"'tE. Bi|noeia: 2aJ5. 2O1. Hexafi y napa,re.neninegiABcDArBrcrD, r.M - ce , fieperrHae rrJrorqfiHy (ABC) no npamift BD. Il.norqr, (AMC) rluicrurl,, tpavy AM i npnivry CC, neperunae (-4- ro AC. Toqna O neperzny npfiMux BD AC HaJresfi i (BDA), i (AMC). To.rxaA,,ranexrurci (AMC), i (BDA or:xe, ArO cnilrna rp.sMa nrrorqzH (AMC) i (BDA'). Bo neperuuae nigpiaor AM y ro-l.4i N. Orxe, N roq nepetu:ry AM i (BDA). 3a4aqi sa roroBr4Mu MarpHKaMu BapiaHr A 1 . Ilpaui BA, BC, MN .ne:*rars n oAniii nroquui, fiKa nep nci cni;rrni Toqnrr rrJrorrluH Jrelrcarb sa AC i roqxa O np D flpami DN i DM teperlu':r.aytruc Mo)fiEa lpoBecrrz nJlorquHy, s vift KB, ae K : DN a AC.lif B n.rorqusi HaJrerfiarb roqrq N M, a otx<e, e uifi renturr, i npn ua MN, arca reperunae (,48C no cni.nrsiit npsmifi KB trroulzlr y ro.rqi X. Toqna X uyHaHa. 3. Fy,4yeMo nepepisr rerpaeApa rrorluHaMri (MNP i (EFK) - qoruprrnyrrrux MNPY i rpzrcyrnnx EFK BilnoeiOo: E ,E aJb a-!b 198. Cri,q ciunoi n.nonlrznu na DC - X, Ha CC - Y, ua BC Z, rogi na nnoulzni (ABC1 - npstwa ZX, ar'a leperrxae -4-B e touqi P, AD - r touqi F; npstma ZY rreperrHa€ BBr y rovqi -8. IllecrNHytuux PEMNKF uryxaunft nepepis i eiu c npasnlstllv, ocrci,rsxn eci fioro eepurrarra - cepeA[Hu pe6ep xy6a i HoxtHa cropoua rooieHloc: KN o Jz. rofi P"= 6 lJr' sarlr.j"2 fhouqa rpaera.rr,Horo rrrecrlnytuzxa o6quc;rnerr'cfi 3a ^ Bxrn6 OopMyroro So = o , .qet -cropoHarrrecrflKyrHrrKa. BI'"El Js so" z,[s ^ztit I n dqlo Toai Su =-'- 4 ' o^z I Bidnoeioa: go1Ql 3{11 . 886 il{: reouerplg Eeee F. fl. ra in. l-lpo$inourafi 2. piBeHb ii:i:i:i:i:i:ii:::iJ:ii:ii iiiii:fii:l{i;ii:*::i: FEOMETPIS Eees f. rl. ra ix. rlpoQ
  17. 17. EF a MY : S, PN a FK : ?. To.rrcrl S i ? ralexaru o6ovr n.norqranaM' orrrce' rrJro- ururrr4 rreperr{Harorbcff no npswrift S?. 5. MN c (BCD), CB c (BCD), MNaCB-X; KX C (ABC, AB C (ABC, KX a AB : Z; AC c (ABC), KX ^AC : Y. r{orzpuxyrnrx YMNZ - uryxauufi nepepia' 7. Terpaeap A,B CD - npaznar,nufi, xorxne pe6po ano- ro a. lllyraunfi nepepia - Aa4NP. $n LADB MN - cepeAurr aiiria, toivry MN =2.2 -- ,l Bidnoeida: oJz: t.lss -2]j1.'8V 2 Eapiaxr E 1 . Ocni.nrxu rA-BCD - ponr6 i rrpsrui CM i CN, .nxi uicrs nn M, B, C, D, A, N.nexaru e oAHift n;rorrlrarri, flrra i To.rfia A Mae ,{erxarrn na MN, 2. Toqrcu N i M Harex{arr, ,4BoM rrapaJreJrbnraM rrpgMu AAr i CCD rogi norra HaJrelrcarb n.noulraui (,4ArCr), i np ma MN c (AArCr). I-{a nrou4raua treperuHae (ABC) npsnrift AC, r:o4i rovxa X neperray npalror MN .nentr . na npalrift -4C. 4. fl.noiqlrna (P.Rl() nepernHae xy6 i yrBoproe nepepia WTPRK.Ilpaua MN J-rexrrrb y nnorqrani (AMC). Cni;rrna roqnax qfix nrnrqun - S. Ilpnua S-R Jrefrr.rrb n o6ox naorquHax. flpone4euo e n.norquui (,4MC,) npslny MN, sxa [eperu npnrry S.R y rouqi O, a orxe, i n;roquny (Pl?K). 5. MN c (DD$), DrC, c (DDrCr), MN .i DrCr: X; KX c (ArBrCr, KX et BrCr: L, KX a AtBl : K, KX a ArDr: Yi Y e (AApl, YN c (AArDr); . YN n-AAt:,$. fl'arzrcyrazx MNLKS - lryrauNfi rrepepia. 7. flo6y4yerro nepepis rrrorr{riuoro (MNP) - xy6a ABCPA PN ^ PtCt: Y, MP a ArPr: X, XY c (ArBrCr), B, e XY, ocri.nrrcu MA, - cepe,4rrfi ninln LXPTP, CrN - cepe4na ninia AYPTP, AtBt i BtC! - cepe4ri .ninii'AXYP,. Otr*te, ruyxanzfi nepepia - qorrrpnnyrHr{r{ MPNBD nnr.rfi e pou6ou, ocxi.nrxn sci ftoro cropontr MP : PN : NEl : MB, e rinorer^y- aaMu npfiMotyrHrlx rpnxyrnrrxie o xareravu ai!. tvtp=^F*--tJt.242 t= o 15 P..-.,^ =4.:=2a45. V LMDP: *O = t, DP = ?o (sa yMonorc DP : PC - 2 ; L. A ZD:60" (LADC - nparrznrnuit), ro4i aa reopeuoro ftocr- nycit: MPz : MD'z * DP2 - 2MD ' DP 'cos lDi *r'=I.{-, }?" cos6oo. MP2=o li-;-l)= *, = +. Ocrtilrrnru LADC : LBDC, ro NP = MP - "Jt36 -ar"[SooJlzIMNP- 2' 6 , Y- 4' 12 , t-T l( alts a li cJt g af a .aJ13 l - tz '4Jrr t2 4)4 L2 l (a ofiB) @'rc ,' o'(a - fi3) =lA-n)l 144-t6- n ' Bidnoaioa: ;. +, ": (s --Jn) . 8. Illyrcanuft nepepis - LMNP. NP l1 BC, SN: NC: SP: Pts:3 : 1; ASNP - ASCB, roai NP: CB: SN : SC :3:4; Np=!a. IcAMSN, rc MS=9, slv=3o, 4 2' 4 IMSN :60'(AASC - npar.unuufi), Ba reopeMoro rcocunycin MN2 : MS2 + NS'? - zMS ' NS MN'=a' *g::-2 416242164 -, t; MP: MN. P,n,=4 +="Ji. p,,,=;J7. , - - Er ",,"-,/; Ji(ili i,)l;e -uu^'I = ,{iaroHa;ramr.r pou6a e ni4piaxr.r MN = AC = onE G BrP = axlS (AopisHroe 4iaroHa;ri xy6a). ToAi sr"ru =tr** . Bjp,sMpN4 = I ",t, ,Js = "'f LBa2 36 cos 60o, Bionoainu: zoJE; ""f. 8. NP n BC : Y, MN ^ AB : X; XY c (ABC, XY ^AD: S, XY a DC: T. Illyxanuft nepepis - n'arraxyrnux MNPTS. (g BBB li{: rEoMETPle sees r. rl. ra in. Ilpo$inunufi piBeHb l{i{tiill;ti*:iii;: ili:iii;i::i:ii*iii::::i TEOMETPIS sees F. Il. ra ix. IlpoQ
  18. 18. Ocri.nrrcra pe6po nyda aiArM : MA: CtP: PC:3: l, ro A-M=?o. ua=!.'44 f ,"^' sa MN=NP=.la'+l ""1=::: 4) 4 _sa,[, fftuo" BoJ2 a 1- E; Ba,JsT.-!Z VJ 8V648832 s,,"." , t-f ,po'-J|i -fi tra*3v6?). Bidnoaida: TW ,z), I'zbJit+e,67). Tecroei gae.qaxHc Tnnosi sagavi ,q,nq KoHTponbuoT po6orra 4. Hexafi y rrpaBrrrbHoro rerpae,qpa SABC SL - 6icenr Ocni"nrnu eci rpaai rlboro rerpaeApa npaeumui Tpux ro SZ - uegiana i nzcora ACSB. IllyrcaHufi nepepia Ae AL sucora AABC. SL= AL -& . 2 ,qe a - cropoH a LACB, roai SZ = AL = *- erf ( 2 v AAS,L: As : 6, sL = AL= 8.r5, p^, = *# = 'ts LBCT (tBCT :90"): BT = = Ja'taG - e)(s,6 - si, s s,[z = s,[, rcNo. Bi|noeilu: 9Ji cm". 6.MLaDDr:X;KXaADTN; ML o D,C, Y: KX n Arb, - Z; ZY r, ArB, : S; ZY o BrC, : T. Illecrznyrunx KNLMTS * r:lyxanuir nepepia. ;rili,i!:.:.:;i:.:. '" r 1..1J:i'l.ll.l.l MS=PT oJ2, sr-3orlz. 44 Pvtprs: ST + 2MS + 2MN, P**n" = |",0 * 2. i"E +, T = rf .+ = lW . r). Pogi6'eMo n'aruryruzn MNPTS na 3 rpuxyrnrznu LNPT : ANMS i pinno6e4pe nplri ASNT. _ "Jn4 Is ANB? (INBT :90'): N? = i2l-a ^la" + -v16 3uafi4euo ttorqy ANP?: o = *' * Y * n', ba oJrs oJz o-4t 4 n 4 -sg-@rofi.'2888 il so ,Jsg alz ( so ,.6s "Ji sa) s^u' 1fl s-- * a it 8o s *-s -T)" l( so oJz ) '!la*-r a JIs*-s ' a- q ) _,li i +-ll- +- i-+- --i, -;-li 8 8 8ri 8 8 8r8 8 8 r8 -8 8 l rT- -z /l I aJeg ,alz) _2sa' ll ( lnY I a,l3s aJ2 | {tt t'sJ-oaJilsl t 8 -8ll= l -z t - .2 =ilfn((Jvi *Jz)" zsl-ft(s-{Jse -.lEf )= - o',C.,tallo)G'ta-ld =# o^=ry oJss B r- z. L + ^alz orl11 SaJz PsNr- 2 4 g ffitsl-loJbe saa Bov2 l s""=1|IJ * s Jt-a - 8 4-)1 + 8' 4 )= 8. Il.norquna (ArCp) nepervHae rpaa; AATDTD no ei4 A,D, a rpaxs DDP$ no rigpiaxy CrD. fltoulvaa (A neperrHae rparl.s AATDTD no nl4piaxy AD', & rp&Hb DD no eigpiaxy DrC. ADt i, AtD treperrruarorbc,s n rou4i O JTflTbcs Hero uaenin (ex giarona;ri xeagpara). Asalor D1C i DCI treperuuarorbcs n ro'rqi O, i gi.narsca Hero ri;r, To4i OrO, .niHia neperuHy trrrorrlriH (ALCp i (A 1 Bi4pieoH O,O, cepeAHfl ninia LATDC, i O1O, = ;4 4C, arli, roai OrOr=ol2 . , ",2rou,Uo, ?12. 2 9, M e (APC).Ilpoee4ervro vepes npami PB i PM, axi rre Harorbcs, nJrorquHy, flKa rreperuHae,4C a rouqi S, r.n ny (ABC) no SB. To4i MB c (SPB). I 2 3 4 5 6 o 6 I B a a , *17a2 - o"65 890 ii::: TEOMETPIS Eees F. fl. ra ix. rlpoQinunur piBeHb i:i:::iii:i:i:i:i:iri:iii:i Iiiiii{ti{iiiliiij rEoMETPtc Eees F. It. ra ix. Irpog
  19. 19. Ilo6yAyeuo nepepio rerpaeApa nrrou{rruoro (APK); (APK) a (ABC): -A-I{. Ilaorqnnu (SPB i (APR marotr cninrny touxy ? u n.norqrani (.48C)' toai Bonrr neperra Harorbcs no uprrrniii ?P. To4i rrpav'a MB rrrrorqrruy (SPB) nepetuHae rrrotr{rluy (.A?K) r rouqi O, gra nanerxrlrr ix cni;rHiit upauifi TP. POSAln lll. nAPAIEnbHICTb nPcMl4x I nrlOl4l'lH v flPOCTOPI S 6, Mmrvro6ixHi inapatenbHi npeMi V npocropi e rprr Br,Irranrr BsaeMrroro poeuirqenna 4nox pisnlrx lpfiMrrx: a) nparvri neperrrrrarortcn (nonu Marorb oAHy cui.nrny touxy i Jrer{carb e oAHifi n.nou{vni); 6) rparvri napa.ne.nsni (nouu He uatots cnilruzx rotror i nentarr n o4nift n;ro- rqr.rni): e) npcui uuuo6irxni (ne nepetnnarorrcg i ne napanentxi, qi npnui Ee Jrelr(arb s oluiii n.norqlrni) IIapare,rr,u i npsui lra nrr' sracru sicrb rpaHcurr'rnnocri. V uaremarurli aiacmu6icmb mpaHJumuaHoclai o3Ha'rae: flKIqo.4effHa e,'ractugictr Br4xouy€Tr,cs A,rIs [apri m I n t qna.napu n i k, To AaHa s,racrueicrr, Bunouyerb- c,xi4.narapwmik, 21 3. IlpunycrlrMo, rqo npaui a, b i c aer*carr s oAHii n;rorquni B, arcift uaaerxar:r rou- xu A i c. To4i nnorqranu u i p neperr.rnarorbcs rro npauifi AC, sna Micrllrs yci rourra flepe'rrauy cx. i [pfiMr.x a, b, c, orxee, B e AC, rqo ne rignoei4ae yuoei. To4i nanre lpunyrqerrns EetrpaBursHe, a orlrce, nprui a, b i c ne Jrelr{arb e oAHifi naorqrani' 214. IlpunycrlrMo, lqo BhliCCy To,qi qepes Hltx Molr(Ha rrpoBecrv n.noquny B, sxifi riaJrexcarb yci ix rovxa. Otrxe, B, e B, Cr e 0, B e 0, Ce B. Ocrci;rrxz roqxn B i C npauoi ArB HaJre)+carb B, ro npaua ArB le:xnrr y B. Ilnorquuu n i B uarom cnilr- ni ro.rxlr 81 iCl, a oTlxe, uarorn cni.nr'ny upniuy BrCr, gxiit na.nexlars yCi cniltai roqrca rrJrolr{zH, rogi A, e BrCr, ulo ire ni4noni4ae yuoli. To4i uanre npurryqeHHfi HerrpaBr,rJ,rbHe i BBr)lCC1. 215. ABCD - naparrerrorpau, ro4i AB ll CD, AB : CD' ABCtDl - napanerorpau, roAi AB ll CrDv AB : CtDr. 3a sracu4sicrro rpanar4rr{Buocri cD ll qDr, CD : CtDr "to4i Ba oar{axoro flapa,aeJrorpaMa r{orr,rptrxyrHr?Ift CCTDtD - na- paleJrorpaM (gri nporia.nexHi ctopoHu qorr.rpr.rxyrluxa rra- pa.ne.nrni i pinni). IIlo fi rpe6a 6y.no 4onectlr. 216. Hexait AA-BC nencurr y n.norqusi c, M e d. 218. y napa,re.nenine4aABCDArBrCrDL AAt llCC1, ro4i n sxa [poxoAt4Tb qepeo Torrxrr A, Ar, C, Cr. Onxe, nJr (ACC,) npoxo4rrrb rrepea rouxy A,. I{o fi rpe6a AoBecrr,r. 219, 3a yMoBoro o ll b. flpr.rnycrnMo, rrro a ll c, roai Ba rrzeicrrc rpau3rrrr{BHocri b ll c, rqo He ri4nonigae y orxe, nanre npunyqe'Hn HerpaBrurbHe, to*y o/". ft rpe6a 6y.rro 4orectlr. 22O. HexaftBaAany npfiMy d [eperr,rnarorb napa.ne,rsni n rqo fieperr.ruarorr,cs n rouqi A, npoBeAeMo n'ltoqlruy c a n rouqi "8. Ilpooegemo t{epe3 rorrxy B n nnorquni cr qepeg rorrny, rr{o He Jre*cr,rrb na npauiit, MorfiHa fipo tpffMy, irapaJre.nrny aaganifi nprvrift i lr,rtre o4ny; npaui c i c'cninna4arcrs, rogi npslra c Jrelrrrrb y n.no oc, i, orrne, nci napale.nrni npaui, axi neperrrHarorb B nprrMy, Jrerr(arb n o4nift ulouqaxi. IIfo ft rpe6a AOBeCTr.r. 221, 8a yMoBoro O e ct, A e d, B e cr., 41 € a, B, e a, A OBt : BBr. rIepea irpaui OA i OB, rqo fiepernnarorbcfl, Ha npoBecrlr riJrorqrrny OAB, a:r"a neperlrnae o no np .4rBr. Posr.nnneuo AAOB: ArB, - cepeAufi ;rini*, A,B,llApi 48,=;AB. . Ocxinrlcr.r A,B, : 3,8 cu, ro AB : 2 . 3,8 : 7,6 (cnir). Bi0noaida:.7,6 cut. 222, tr1exaft rpr.rryrnr4r{ ABC nextvrs y nnorqr,rri a, O A, e a, 81 E s,, Cr e a, A - cepeAnHa OAt, B - cepe OB1, C - cepeArrua OCr. r{epea nparrni O-4, i OBr, rq perraHalorbcs, MorfiHa npoBecrrr rrJrorrlr4rry OArBr, nxa Tr,rHae o no npamift 13. Asarori.rno trronlrna OC,B, Tzuae o no npauifi BC, n;rouqrana OA'C, nepernnae npnrvrift AC. V LOALB..43 - cepegna nlnia, AB =L4z y LOBTC,BC * cepelna ,rinis, BC =I",",, y LO ec =!;*c..2" Otrxe, P4^c, = 2Pag,, repr,rMerp LArBrCt ygeivi 6i.nrn Bidnoaido: y 2 pasu. 223, B:iz-napox 1. Bigpiaox/Il rre neperr4Hae BaAaHy rrrro rca). 3a 4one4euvu y aagaui 220 npattiAArll tutlVtrllBB ro4i rourcra Ar, Mr B, .nexarr ra o4nifi npannift. AA.B AAl i BBr. 3a reoperroro @a'neca ArM, : BrMr, ocHi.irrnz AM : B rpaneqii i MMl=4:tu', MM,=6'5!8'5 =z,b Buna4or 2. Bi4pieox -u? .r"o"tr"u" ,uou"f, rrro*"n AAtll MMl l] BB, i.nexarr s oAHifi nrorurani, .fiKa trep iiii;ii:iliiiii:;';:j TEOMETPI9 Eees F. 11. ra ix. flpoQ l11.fg,+t:rj,:.:d Togi BC c c:.', A e. BC. Ilpaua MA neperutae c n ro'r4i A, iii*F.i:i:i:.::i MA e ct. Maeuo: BC c o., MAr.epern:,l,ae a s ro"iA, A € BC, :l{li,::i#;: roai MA i BC - vrr.mto6ixui. ;ll$iif$ji:ll ToqxuE eMA,Pe MA,F e BC,K e BC. Ilpanti,4?iPKne' il$i*:i:iii!:: perr4Harorbcfi r rovqi P, roAi'repes Hr'Ix Molr{Ha npoBecrt{ nlrlo- l:iiiiffi:lii:i: urn'y 0. Ififi rnoquni Harrenrrrrr' to'rxa.E (ocri.rrxz E e AP) ;:l:'.!jili;:iii:i i ue sa,terxxrr ro'rxa F. ToAi npgma -EF neperunae urorqrrHy B n rouqi E, E e PK. Onxe, npaui PK i EF - mumo6ir*si. 217. Hexafi napaJreJrorpaM ABCD ner"urt' y naouluHi cr. 'Ioai BD c o. Ocrci.nrrn b ll BD, ro qepes Hn x Mor(Ha npoBecrtr - rrrorquny. Ce b, Ce a, ro,4i bc cr,. Ornte, npsua bJlemcrrrb y n;rorqrani cr, flpflMa 4 fieperrrrae cr n rouqiA' sxa He HaJrexc]rrb b.'Ioai a i b - nurvro6ixcni. II{o fi rpe6a 6y.no AoBecrr. as2 lt{: rEoMETPlg 6eeg F. Il. ra ix. rlpo$insmnfi piBeHb il{iil*iiiii:iiii:::i
  20. 20. ripfiMifiA1B1 i M, e ArBt. Branonaeuo napaJIeJTbHe rrepeuecenH,fl nigpisxaArBr y Ha- npami .4-4, na ni4pison -4Ar, o,4eprcr.ruo ni4piaon,4-Br. ArB,ll AB, ArB, : ABr, AA.B82 - naparerrorpaM, Bp2: AA. Ilpogonxzuo MM, go nepernuy a.4Br, vaemo M, e AB, AMr: B"Mz, M1M2: AAy Posr.nsHemo LABtsr: MM, - cepeaHr liniR, l,rtr, = |nnr; BB2: BBt + r,1r.2, BB2: 8'5 + 6'5 : 15 (n); , M" Bt MM2: 7,5 m; MM, : MMr- M'Mr, MMt : 7'5 - 6,5 : 1 (nn). Bi1noai)a: 7,5 r,r a6o 1 u. 224. Bzna1ox 1. Bigpiarcu AK i BM rerr{arb B oAHoMy nienpocropi ei4uocno o. . AK 1J BM, ToMy qepea Hux Mo)fiHa trpoBecru trJrolrlr4ny' .flKa Mae a oc 4ni cninrHr roqxlr A i B, orrxe, qi n.nolluun neper[HaK)Tr,cs lo npamifi AB. KM c (AKB), ro4i roHa neper.rrua€ c n rovqi C, axa sarerxzrr,4-8. PoarnsHeuo LCMB i LCKA: eoll.u no4i6ui sa 2 nyramu (/C - cninssufr, ZCMB : ZCKA aH ni4noeigni rpu BM I KA i ci.rHifi I{C), ro4i + = rytypaxoByrcqr,'' AA KA" q + =93, ru yuonoroAC, : CrB, : 2 : L i BB, :AB1 BB' o'*", l=-99', a", -8A';372 AB AA e) _ = ^^ : aa yMoBoro AB : BBr- 4 :3i AC - m BB, CC, 4mBmoT?fie. -: UL. = -3CC,'4 )aA BiOnoei0o: a) 9,6 4u; 6) 8 ,qrvr; e) 3m 4 tto AC - BC - g. *u"*o, -qC 12 =3, sei4mn: 4BC - }BC t 27, BC - 27 cv' ior,iAC-36cu. Bc+9 16 4 Buna,4ox 2. Bi4piaxu AI< i BM Jrercarb y pisnux nienpoctopax ni4rocno ctc. Il.norquHa, il{o trpoxoAr4Tb vepes AK ll BM, nepetrzn ae a no AB; KM uar'ex"urt' 4iil nnorqrzni, ToMy Mae touny C neperuny 3 cx rafiy, u{o C e AB. LAKC - LBMC Ba ABoMa HyraMu (1ACK : IBCM sH BeprnxarlbHi, /AKC : IBMC ax nHyrpilini pienocro- poHui npn,4x I MBi ciqHiitKM.Toai { 11 uo".'MBBC xoByroqrr, qo BC : AB - AC, BC : I - AC, uaeno: 16 =!- L, sag.86-7g1C,1AC-86, AC=5: L2 3 q-AC I 7 Bi1noeida:36 civr a6o 5- cnn. 225, Oct<intxuAArllCC, i] .e-Ar, ro BoHu rre)fiarl' n o4nift n;rorquHi 3 trprrMoro A'B'Ia 226, flapaterHri upaui CCt i BB i npaua-43, rqo ix neperrnae, Jrextarr' B oAHla rro- n1zui, axa neperfiHa€ a no npauifi ABp Cr e -4-Br. Tpurcyr- uunu ACC, i,4J3Br no4i6ui 3a ABoMa rcyraMrr (1A - cni,lr' uufi, IAC.C : IAB.B ax ni4noei4Hi npu CC,l] BBr i ciunifi ,4Br). To4i: AA CC. a) -" = 4; ea vMoBoro AC : CB: 3 :2 i BB, : 16 4u,'AB BB. 3 cc. 48 orrxe,1- -]; CC, - : =9,6 (AM): 5165 227. SayMoBoro g =2, rogi, axrqo r - ix roe@iqie"BC2 Bx, BC - 2x cyt. KM = *, =+ cu, ocnirsxu KM cepe4Hi risii LADC i LADB i KM llAD ll eN. Xe : M ocxirrxu KP i MN - cepe4Hi aiuii M-BC i LBCD, KP tl M N ll sc. P,,n"n ' (t; ,*) = ur. Ba yMoBoro Prrro : 5x : lO, x : 2. Toti AD : 3. 2 : Bidnoeidu:6cui4cm. 228- NlMt- cepeAns niuis ACDB, *r*, ='+ = 10 (c P,M, - eepeAHs nisis LADB, *,=+= 8 (cv). AHaroriqso KrPr : 10 cu, KrN, : 8 cu, roAi Pr,r,v,q = 2 (10 + 8) = 36 (cM). NM - cepe4Hr;rinis AN,DM,, NM =ry = 5 (cu). AnaroriqHo KP - 10 cu, 2 KN cepeAHn riHin rpane4ir K.ADNt, roqi KN - 1 rrJronltrHa rreperrzHae oc ro npauifi A.BD Ct € AlBr 3a yaa- ^ I ia.nr,seHoro reopeMoro Qa:neca AC i CB : A$r: CrBr, or:ne, A :4-t I ArCr: CrBr: 2 : 3. flrcqo ix Hoetbi4ienr nporopqiitHocri J. _ ,1--1-_L ro A,C, - 2x, CrBr- 3x, ro4i A,B, - 5x i ArB,: ArCr-- / I I l) Ex:2x b:2. > A, C, B, Bi0noei0a:5:2. '--> -f.t{z(-"/ / 24eBC jii.r.. -. . ... , Asaroriqso PM : 12 (cm). To.4i Pruv":2.(I2 + 5) Bi}noeidu:36 cu; 34 cu. 232. a) flxu1o M i i/ e6iranrr,ca, ro npsui.4-B i CD nep 6) ,flHr{o M i N se a6irarorrca, ro npama -4-B Jre)fitrrb a rrp.ffMa CD ne netxur; y nifi; npsui AB i CD M 6iatsi. 235, 3a MarrroHxoM 87 nigpyuuuna AAr ) BBrll CCr, A, rerorpaua-43CD ro.rna treper[Hy 4iaroHa,'refi O; vepe 4e 0, e o. PosusHeuo qorr,rpur{yrHrr}c AACC.. Sa yu orwe, ATACC, - rpaneqia. O - cepe4rana AC i BD. uoro @aneca O, - cepe4zHa AtCl i DBr V rpaneqii /A ss ainis. oo. A4*cc' . oo. =32 - 16 t.*t.'22 Poausneuo LDBB; OO, - cepe4rr ,linia, OO, - ! "BBr: 2 ' 16 : 32 (cn)' ------'-' --t 2" Bidnoei1u: 32 av- iiii{iilliiill:iil{i rEoMErPls Eees F. Il. ra ix. IlpoQ 894 i::::: fEOMETPI9 6eBs F. l-1. ra ix. [Ipo$inuxufr piBeHb :;:;:;:il;:;:;;;:;:;:i1:;:;:;:;:;:
  21. 21. 236. 9orupuxyruux AtACCt - tpaueqis, oo, - cepegua .ninia, oo, = &:cC', ari4xu -AA' + '2 + Ccr : 2AO. V rpaneqii BTBDDI OOr - cepeAss ,'iinis, roai oo, - BB' ! DD', asiArcu BB, + DDr: zoot. 2 a) Bnafi.qeuo cyMy ,4oBlr{r4rr ri4pisxin AAr + CCt + BB1 + + DD1 : 2OO1 + 2OOt: 4OOt.II{o fi rpe6a 6yrlo AoBecrl.r. 6) Cyrraa.AA, + CCt : 2OOt, cyrr.a BBt + DD1 : 2AO, rogi' AAt + CCr: BBr f DDr, rqo fi tpe6a 6y,ro 4onecru. $ 7, IlapanenbHicrb npeMoi i nfiou-[nHl,t V npocropi BBaeMHe poarrirqenirr npamoi i fiJrorr{r4urr uolrte 6ytr'r raxum: 1) npsua rerrcurt y n,rorurHi: 2) npsua neperr4Hae nJrorqnny; 3) npnrvra i n,roulrua He Malorb cni,'rr,nrlx roqox - np.*ua i nrot:1una napaJlenb- ni. flxrqo nprua napaJreJrbHa Aearifi n.norqlrni, ro arepeo 6y.4r,-sny rovxy qiei nnoqu- r{n MorfiHa npoBecrrl npfiMy, rrapaJ'renury .4anift, i go roro rx ri;rrxy o4ny' ,flxrqo npama, sna He Jrelrir4rr, y txo4nift 3 ABox [JIou]]rE, tr{o neperrrHarorbcs' na- paJaeJrbna niHii ix neperxEy, To BoHa napareJrbna rcoxtsifi is 4a-Hux trJronlnH. .fku1o npalra napaileJ*'Ha roxnifi ia gnox u;rorqrn, rrlo neperr,rnalorr'c,F, To BoHa trapaJreJrbua ;risii ix neperfiHy, 251 ,AB ca, DCllAB,ropi Ba osnalcoro napa.nearuocri npalroi i rrJlorqrrHrz C.A ]l rri" 252. Hexatr rrJroilIrsa cr neperr{Hae trroqr,rHy rpane4i A,BCD no nparriii, ,sra uicrrzrr cepeArrro .rirriro MN. Totl MN c a, BC ll Mlr, orxce, BC ll a; l,o ll twn, omne, en ll a. II{o ii rpe6a 6yno 4onecta. 253. r{epea npsnri OA i OB rroxtrra npoBecrrr flJrorr{r{Hy, ffKa reperrrfiae rrron{rrHy c no nprnrift AB . V LAOB MN - cepeAr{s.ninis, Ae M - cepeguwa sigpiexa O-4.' N - cepe- Arana siApiara OB. Ocxiarnn MN ll AB, ro MaeMo: AB c a, M N I AB, ro,4i sa oanarcoro fiapareJlbHocri npauoi i nlo- Toai n l] z sa raacrasicrro rpansurlrBnocri, i rvraemo Ha d, rrlo npoxoAr,rrb rrepea npsMy r??, ilapar'reJrbrry rrapa!'reJrbua c, mll c, Ocxi.nrrn mll a, ro c ll a. tl{o 256. Ocxi;rr,xz BC jl cr, ro nrrorqrrua LABC nepenunae napa;re.nrnift BC, rowxa N na.nelxzrr, qiri nparrift, Togi MN ]l -AC i ea reopeMoro @a.reca N - cepegu MN - cepe4rs fi:uir, LABC. a) Ocxilrrcu MN : a, ro BC :2MN : 2a; 6) LAMN o A, -BC, Mll - cepe4u,x nini.s MBC, ro AeEUM y aagaui 254 Sr."" i S-r" : 3 : 1. Bi0noai0u:,,a) 2a; 6 3 : L. 257, Ocxinrxz M i N - cepeAuHr4 AB i AC, ro MN - ninia AABC, MN )l BC, ttN =|nC. Oclci.nrxu MN BC ll MN, ro 3a osHar{oro napa.ne.nsHocri npnvoi rqnnra BC ll o. Hexafi AB - x, rogi AC - x, BC - rnli, ** = + D _' *.rJi 22 2x + xJi AO:)2 2x + SxJiP"",r"=2 L+'Ji-+= x"li("li + 2' P",,," i P,* - *Ji('E' + s)' QryA = Ji + a : Bi]nosi0n: Ji+s lr.L' tTzuw MN ll a. IIIo fi rpe6a 6yao goaecru. (0 254. K€ o, P€ cx,, rosi I<P c a. v MBCKP- cepeAng U{),riuia, KP ll BC. To,qi Ba oauafioro napa.ne.rrnocri npsrroi i naorqrauz BC l] o. IIlo it rpe6a 6y;ro goeecrlr, LABC * MKP sa ABoMa KyraMn (ZA * crl-iaruufi, ZAKP : IABC g.t< siAnosilni npu KP ll BC i ci.rHifi -4,8). Toai: a) P*" : PAK.: BC : KP : 2 : 1 (sa n,racrznicrro cepe4nr'oi linii rpunyrnura); 6) S*" : SMp: BC2 ; KP2 : 4 : t; n) e nonepe4usoro Brtfirr.rBae, rlo Ssc : 4S*0, rogi Sr""" : Ssc * Sn"": 3Ssp. Otxce, maeuo: S*n : Sr"r" : Bidnoei1t: aJ 2 : l;6) 4: 1; 3) 1 : 3. 255. Ocri.nrxia o ll cl, ro r o icrye npama m, m ll a; osri.nrxr a ll ts, ro n 0 icHye npswa n, n11 a. 258, OcHimxu a l] fC, ro cx treperr.rna€ nrrotr{rny A"ABC - uapa-ne.nr,uifi BC. Togi NM..)l BC i aa reoperuoro (Da,'re roti NM - cepeAun rinis AA-tsC, XU =LBC.'2 3a yuoaoro BC : AC: 6 : 8. flnqo r - xoe(piqienr ix nocri, ro4i BC - 6x, AC - 8x, nN =!1rC, AN -2 l1 NM - 3x- ^S..... = - NM . AN, S",. = -:.3x.-lr= 6 2 -*' 2 --- --- rogi 6x2 : 24, x : 2, AC: 16 crr, BC : 12 cv,, AB pemn fli@aropa). CM - ue4iana trpffMonyrtoro rpn 1 reuy3fl, orr+ce, CM =: AB, CM : l0 clr. 2 Bi1noeilt: 1,O cw. 259, 3a MarrourcoM gb ni4pyvnuHa nnolqunu (ADC) i (ABC) ileperrruarorbcfi no npamifi AC. Hexaiz M, N, K, P - cepeAuHrr ei4nouigno .nauox ,'raltanoi AD, DC, CB, AB. y LADC MN - cepesne ;riuin, rofi MN )l AC; y MBC PK - cepe4irn aixia, ro4i PK ll AC. iitl:iiiiltl{iliili TEOMETPI9 Eees F. It. ra in. Itpo 29 yct rAq 10 u., c. I 896 l{ii reonerpls 6eee r. tl. ra ix. rlpo$inrnrft piBeHb {:i${t{ili:}:':l:liii
  22. 22. 3a eracrueicrrc rpaHslrrtrBHocri MN ] PK. {epea napa.ne:rr'ui npami MN i PK rron*ra ilpoBecrr nrrorquuy (M N P), ro1i M e (M N P), N e,(M N P), K e (M N P)' P e (M N P)' II{o fi rpe6a 6y,ro gonecrrz. 260. Hexafi roqxa M - cePe4Iana PB. V rpaui PCB vepea rouxy M npoBegeMo MK, n rpani APB - MN, K e BC, N e ,4-8. {epes MK r MN, anine- peTuHaroTbcs, npoBeAeMo uloilItrHy' gHa neperr{Hae rpaHb ABC no N K. M K c e (N M K), M K ll PC, romv PC ll ftt twxl. n Ana,rori.*ro PA l] MN, roal PA l] (NMK). ocxi;nnu M - ce- pe1nna PB, ro 3a reopeMolo Qaneca MK - cepe4ns liHia LPCB, MN - cepeAns riuin AAPB, l/K - cepe4Ha aiHia '1 A, _BC, roai MK = NM = NK = rAP =3 cv. Bi}noei)u: 3 ctt. 261, Hexafi cepe4una BC M, roni civua n,toquHa treperuHae rpans BPC no PM' flponegeuo n n.norqugi (ABC) MK | ,43, roai K - cepeguua AC, MK - cepeAHs ttirrist LABC. CivHa naorqr'rna treperuHae (APC rc PK' ToilLKPM - ruYxaunfi nePePia. t<tw =!a: BM -9, PB : b. Ocxirsxu PB : PC, ro 22 LBPC - pinno6egpeuufi, rogt PM - Brrcora' ue4iana' Ia LBPM (tPMB :9O'): pu ^fa" ": =.E - = ur. !4'l/4 V pinxo6e4peHoruy APKM npoBeAeMo Bzcory' uegiaHy PO' ls LPMO (ZPOM :9O"): 263, Hexafi y rerpaegpaABCD M - cepegrzna BC. flponegemo n rpaHi ABC NM -4C, n rpaHi BC MMrllDB. flpone4emo naoquay (NMMr), rogi N,M, NN, l] DB. gornpnxyrHun NNIM.M - uyrauuii nep MMr , cepeAHs nnis LCDB, MMlll BD, lttttt, = NN, - cepe,+Hn ,riuia A-A-BD, NNl ]l DB, **, = V vorzpzxyrHuxa NNTMTM MMrl) NN' MM1 : ro4i aa oaHaxoro traparerorpama NNTMTM - fiapaJ 264. flxrqo civua nrorqnHa npoxoAnrb uepes M flap MK I A,D, K e CD. Ocxinrxu ciuua uorqzHa tra KL ll BC, L e DB.Ilaorqzna, u{o trpoxoAzrb uepez no MN ll BC, rpaus ABD no N-L. To4i MKLN - naparerorpaM (KL - MN. KL I MN KL MN 3 s."r, : 2(KL + MK), P.Kr.^ MK = NL =!to =!o.11 d z(?t *!").lD o I d o / - z(?t *!')J n / 1 Toai S*"" =;U* POi S,ro' t-; -tlh' 5a' Bidnoeidu: * E; J a lb- 5a' 262, Hexafi y xy6a ABCDATB.C.D. eepeguna AB - rouxa M , cepeArrHa AD - roqna N. Ocxiarxu ciuua nlorquHa napaJrerbHa CCr, npoeegemo n rpani AA'D.D NN1 | CC1, e rpaHi AA'B'B MMrJl CC', ro4i npsuoxyruntt MMTNTN - uyxanzfi nepepia. NN,_AB- r,AN=,, o*=1,t2 ro4i is nparroryruoro rpuxyrnutta AMN (IMAN : 9O"): MN = L,12. 2 orrxe, p.*"". = 2(NN1 + MN)' Pwv,r," = , (.,. L,tr) = tb t Ji). Suv,.u,N = MN NN,, Srr,,.' l,t, ,=t'J' Bionoaiua: ilz*"E); 11? 2 . . - -. - - -. - r..r;.:r:'j 898 :::i::: rEOMETPIS Eees F fl. ra in. flpoQinumufi piBeHb l;:;:;;;:;:;:;:;:1:;:;i;i1i;i;1;:; BiOnoei0v: 266. 3a MaJTToHKoM 96 ri4pyvHuxa allU, a c a, b cB flpirnycrrzmo, .qo ca. flpaui c i a.nerxars n o4Hi pa,Terr,Hi, To nepertrHarcTrca. To4i b c B, rpsua o 6irrni, rqo HeMolnJrrrBo, ocxi.nsrz Ba yMoBolo a ) b, ii rpe6a 6yro aoeecru. 268. Hexaiiunmo6ixsinpnlriaibpoanailleniynpocr - nrorquui o, a b reperuHae rrro n,ronrnHy s Aesniii npnMy c, c I a. -Iepes rfaui b i c rpone4emo nro gepea rouHy B npamoi b npoee4euo npsmy c', c'll ocHinsnz c ll a, c' l) a, ro c' ll c. 3a Aoee4eHzu paH npaui, ari neperr4narorr, oAHy B ABox npfiMnx, rqo TzHarorbcs i napa,reGui gpyriii npauiii, Jre}Itarb e n.norquni. Orrxe, c i c' .nenrarr n o4Hifi uouqnui. I{e ArfieHHfi npaBffJrbHe 4ra 6y4s-nxoi trpfiMoi, ilr,o nep b i napaae.nrna a. IIJ,o ii rpe6a 6y.no AoBecrE. 269. r{epea npalnry AC ll q npoeeAesa trroiltruna (ABC) NM l) AC. Ocnimru M - cepesirga BC, MN ll AC, otr =r KM, oM = 2 a 4 , po = '[ill" - otw", Po = 1 2 r;- -!b' - ba' 16 A1 cepeArlHa BC i MN cepeAH.fi ,rinis AABC, Nl,f = CM - me4iana, [poBeAeHa 4o rinorenyalr, roaiAB AR : 2a. BavmoeooBN NM o. BN loc o. BN' 2 2 2 BC : zBN, BC : AC * a. 3a reopeMoTo fligaropa -4 4a': (AC i a)2 i AC2;4a2: AC2 + 2a AC + a2 + 2AC2 'l 2a . AC - 3a' : 0; sexafi AC x, rogi 2x2 $l::i:*:iiiitii{ii TEOMETPI9 Eees F. l-1. ra in. Ilp 29*
  23. 23. xt,z = ' rt,z fE I a a|'l ,2a!2oJ7 _l 2' 2 4 | o a.,17 l-:- *r,-<0. 12 4 -Zotrlio" +Zlo" ornte, AC ="Qvr-r), "* =t +!+i="'li -f +2" =+! L@ -t ellIA ^ 2 4 a'0-l)_3a' *Mc2L68 BiLnoaila: {. 27O. flrnorsqrra:l u, F, y raxi, u1o s ll AD, F 1] nn, y AD, roti M,N, c a' *f 'N, ll An, MrNrcg, MrN,llAD, M"Nscy, MrN" ll AD, orxce, MtN,llM2Nz ll MrN.. OcxitrtxuAMr: MrM": MA[r: MrB,ro zareopeMoro @a.neca DN, : NrNz : N2NB : NsC. Maervro: Mr * cepe- gul;.a AB, N, - cepeguna CD, M2N, * cepegHn liuia rpaneqii -A-BCD, rogr M"N^ = o * b t2- z ' M"N" - cepeAgfi .ninis rpaneqii MrBCN", roni ^-a+bq Sb+a lI{-N^ = 24 MrN, * cepeAn,n .ninis rpanegii AM2N2D, roAi MlNl = Ilpoaegeuo sucory BK rpaueqii BK i MrNr: Ki BK n M"N2: Kr; BK r' M"Nr: K". 3a reopeuoro (Da.neca KKr: KrK": KzKs: KrB' To4i: a) s.^^^ =o'b . BKz K.K. =BK.-1-mrD.2".-.--1..3-2, 3a+b 3b+a .s.-.-.... .BK =4a.+:g.u{ ="ru."*,"v,vrNs^r224.224 n o*2.nrc Dv,v.v.v, 4 I . s* 2 s*" =f,zlc-nc, a+b a+- t 2 3a'+ b 4 6) KK1 BK 4 xra = ff; 3a+b A +o BK 7a+b Jev.r',o= 2 4 - g BK 4 7o *b .BK. - 3b+a * =r+___', BK _7b'a.FK=!!J".py.*u38.^J249432 so",,., _ (7a +b . BK,(7bn o ax) =7"*b . sr,".u, 32 / 32 t Ib-a Bilnoai}t: a) L : 2;6 (7a + b) : (7b + a). 9oo iii: TEOMETP!9 Eeeg F. fl. ra ix. Ilpo$inuxui piBeHb i#ilii;:*iiiiii;i 271. Ocnins<n ,BC ll AD, ro BC ll (ADM). flpoeegeuo uepea npamy BC i rovxy P n.norqzuy (B Ocnirsicr BC (ADM'1, ro (BCP) . (ADMI: PK, Ae K € DN, i PK 11 BC, a orxre, PK ll AD. 272. M € (ADB), N e (ADB), M i N nanetnarr ci nnorillrni. Ocxiar,xlr q,fi rrJrorqrana napare.nrHa BC e Hifi e np.rrMa, .sfta [apaJrerbHa BC. flpoee4elto BDC NK l) BC, K e DC, KN Jrer{rrrb y civniii n.n ToAi qs nroquxa neperuHae tpant ABC no MK. LMNK - uyraunfi nepepra. Ia pinnocrbponnroro ACDB: Vpaxoayrcvz, uro DM : MB -- uaerro: DN : DB :1 : 4, KNDNA BC DB '1:3. .KN 1 ---- a rofi n = i, ** = : , ocximxu ADNI{ N LDBa Ia pirnocroponnroro AADC maouo: lD : 60", MD ls AMDK sa reopeMoro xoornycin: MK'z : MD'z + D MK'-t *o'-2.a.dcos6oo: MK'z=5o: -{.4 16 2 4 16 8 MK = yF. LMDK:AMDN ea 4noua croponalru i 4 na, DK: DN, ZMDK: IMDN). {vur: NK+2MK. P*,*=t-, +=tn."f lo -!*oJB " - 2.w^( 8' 4.-^vLK '!t e' a Jtgn 4 2 -u64 oh - z,li a' Ju _Bidnoqidb: n t On 273. Ilpone4euo n rpani CDB NK il BC, K e DC. To4i pea roqrcr M i N i uaparrer'rbna 8C. Illyxanzfi nepe TpuxyruuxuADC,ADB, CDB pinni, pinHo6egpeu moryrni. AD : DC : DB : b, rofi AC - AB = BC nn -r oc. DN =2= DK. rorj NK=b {2. 4""' "" 4 ""' 4"-' ls LMDN (ZMDN:90") DN ro'i MN = g;* =i,ro LMDN : LMDK sa ABoMa cropoHaur.r i Hyrom uixr 41* r.!^1* o*r-=# ='fi *lJro. illiiitliii;iiii{.::11 TEOMETPI9 6eeo F. !-1. ra ix. Ilp =i'*'=?i (""ls "( oJs a a' t-+_il -_-t.- 4 8/ 4 A) I' az a' 16 -64
  24. 24. LAA.C M - cepe4fiHaAAr, - Mo ll A,c, roii (ttnn) e,c. Mo = ! 7..C, Mo = !; so . oJ2, a" a - cropoH 2' 2 Fof* o,trt, u{ro u,fzt tu,tif =1/t +'s-ll q--a Jlnl= uJz Ew' ufz u"E.Jtg = e ! o+ = a.s ArC2 : 3a2, a2 = ={.'ooiBo=!!Z.s/^. .--- -- t^ !J !t d3 3' 2b"hg b'^lG 64 32 ^ ldJtd a',la Duao=i'-Js'z- tT' Bidnouidot d'JG . ,12 S 8. flapanenunicru nfloullrH 274, Ciqxa nrroulqHa neperunae (ABC) no CM . Hepes AD i DE ' ilIo neperuHalorbcfi, trpoBeAeMo nnor4uuy ADE, sxa treperue ciuny naorqzny s touqi O' CM aAE : O' ITtorslnuaADE trpoBeAeHa qepeo npflMy D-8, napa.nellny ciunifi n;rolluiri, ro4i eoHa neperuHae ii no fiaparerbHiii npamift. flpone4emo OK ll DE, K e AD. Tofi LCKM - uvxaHuii nepepie. (CKM ll DE, C e (CKM), M e (cKM). A 275. Ilpone4eMo qepec BrD i M l:.ttottluny, srta neperne civ- Hy nJTonIuHy no npamifi, napa,relrniii BLD, MO ll Bp, O e AC.Illyxaunfi nepepie - LAMC; ABCD (BaApar' flpalra, ,fiHa jreJfiurb o o4uifi s ,qBox napaJreJrbHux nr nrorquni. ,fLcqo Ani npami, xxi fieperfiHarorbcfl, o4niei filaoqz 11wui, ro qi n.rorqzHn napa,re;rrHi. ,{ri naorqzHu, rapa.ne.nrni rperifi nnoiquHi, naparen gepea 4ri naparersHi npsvi moxua npoBecrr'I ffJro OAHY. t{epeo aai unmo6jr+tsi npnui uoxHa npoBecrn trapy n roro:x ri,rsnn o4ny, Ilaparemui nJrorquHn, axi neperuHarorr gani npRui nopqifiHi eiApisnr.. 288. Yepee npoueai S.4 i SAr npoBeAeMo trroulllHy ( ffxa neper[Hae o, B roqnax AiAt, a orxe, [o npxv a B - n'rouqi B no npauifi, u{o trpoxoAurb.repea B lli neperzHy ,4Box ilapaJaeJrbHr{x nJrorqun Tperbolo r Horo napaJrelabHi, rolty [poBeAeMo n B vepes r. B naparerr,Hy -4'4.r i anafi4eIvro roqr{y Bt ii neperzuy veuev SA,. 289. V n;rorqzni o npoeegemo npxuy a' rafiy, ulo a'I a, flHy trp.rrMy b', rqo neperunae a'. flpone4emo upauy To4i.uepea npalti a i b MolfiHa fipoBecrtr nnorquny napaJ'IeJr6Ha d Ba oaHaxoto napa,le,lurocri nJouthH. 29O. flpunycruMo, ulo n n.norquui o( e rrpaMa cl, sl{a H nae B, ocxinrnrz cr i p piaHi. ToAi npsrra a uae cni.n Ha cx, Mae cninruy tovy a B, ro4i cr i B nepetzuarorr Orxte, Ho:xua [pgMa [JIorqIzHu tI trapaJreJrr,Ha n;rorq 291 . Ba MaJrroHKoM 107 ni4pyunr.rxa Br - cepe4vHa O pe1usa OC. Yepea OB i OA nponeAeuo ruroqrHy (O.4 AB i AtBt raxi, rqo.4-B llArBr. Aaa.roriuHo nrorquna AC i APl rar{, rqo AC AlCr V n,roiqzui (,4-BC) mae perrrnarorrcfi i aignoai4no naparelsni npsmurr -4rB treperuuarorbcs, Ba oanaxoro napa,re.nrHocri nrloqrlH 6y,ro 4orecrz. 292, Hexafr. O - cnirssa cepe,qnua nigpisxis AAb BB n.norquHi. flpone4euo vepes ni4pisxu AA1 i BBr iilii:iiii:::iiiri::$ TEOMETPI9 Eees F. fl. ra in. Ilp AC = b8. te LBMO (tMBO:90'): *" - ;, no =$; l;l z* J" %' LAM| - piu"o6"4p"""ii*o'loi q -- 2 r (AM : CM), MO - nucora, ue4iana. S*r, = : AC'MO, t - ,[7 . zt' oJio +u' -hl"r. - "wtqa - - b,l2a' + 4b" Ridnoaidu: 4 A, ,.;.-:al.1i!l 276, rlpoee,qeuo n (.4-DD,) I'{K ll DD,, e (AA,B,) ME JI DDb K e AD, -E e /3. Ilrvna- nuii nepepis - napaJrerorpav EMNK (EM ll NK' MN ll EK), NK :"ME : a' Ia LAEK: 14 - 60', dz=lan. AE=a. ax=li;4--' 4 4 EK2: AE2 + AK2 - 2AE AK'cos 60o; EK" =L*no' -2 I ?" !, 16 16 442 uu" =tgr:u" (, "*, =#. "" =* A t a{7i ,(rc+"?) ToaiP."nn=2lo-16J= 8 Bihnoeiva: o(ro * "[) . A 8 277. Illy:rta:eufi nepepia - LMBD' l flpose4euo uepea ArC i rovxy M nnor4tny,;rra rre- perruae (MBD) rto MO, le O roqna nepetrzHy BD i AC. 902 i:i:j: |-EgyE1pl9 Eees f. l-1. ra ix. npo$insxufi piBeHb ::iii#:i:i:i:i;i:i:i:::i;i:::::
  25. 25. i LA.OB1. Bouu pinni Ba ABoMa croponaMr{ i xyrou uiuc nramu (AO :40, BO : BQ Ba yMoBoro, ZBOA: ZBtOAl ax neprnra;rr'ni). "loyi ZBAO: IBA,O i aoHn eayrpiurri piauocroponni npu npar,rrx r4-El i ArBr i ciunifi r4Ar, or){te, 3a o3HaKoro napa,re.nrnocri nparvlzx .4-B ll -d.rBr. tlepes si,4pis(rr BBr i CCl npoBeAeMo n,rouluuy i poa- rJlfiHeMo LBOC i LBTOC. Bonz pinni Ba ABoMa cro- ponaMr{ i nyrou rrirrt nranlr (BO : Bp, CO : CQ, ZBOC - ZBtOCl ,nK Bepruxarbni),rogi IBCO: lBtCtO i nonu rny'rpiurni pieHocroponni npw BC i BrCt i ciuuift CCr, orxe, BC ll Bpt. Maemo: e n,rorqzni ABC npani AB i BC flepertrHarorLc,n i ni4noai4uo napa.ne.nr,ni upr- vzvArB, i BrCr, axi neperrrHarorbc,a i lerxatr y n,ro- t4uwiArBrCr. To4i aa oaHaxoro napa.ne,rrHocri rrJToIr{uH @BC) ll (AP{), qo fi rpe6a 6y,ro 4orecr:u. 293. 3a sracrunicrrc rpauszrrBnocri, axllo o ll V, 0 i] V, ro cr ]i p. Otrre, cr i B ne uorxyrr neperrrnarrrcs, 6o eourl napa.ne;mni. 294. AoeeAenfio, rqo srrqo rJrorqr,IHr4 B i 1 napa-re;rrni i naorilzHa o nepertrHae nJrorqu- ny B, ro BoEa neperrzuae i nnorquny 1. flpranycrrnrro, qo o( ftepernuae 0, a.ne ne fieperrrHae Y, a orxce, o ll y, 3a n.nac- rrznicrro rpaustrrr{Buocri: arrqo cx ll y, a y I B aa yrroeoro, to a ll 9, rqo HeMorrcrruBo. Togi cr neper:vnae Y. IIIo ii rpe6a 6y:ro AOBeCTh. ,[ore4errno, rqo fixqo [p,fiMa o neperrruae rrJrorqr4uy o(, To Borra reperr{Hae i n.nor4nny B, axulo cr ll p. a a a : A. Ilpone4euo e llorql'ni cx, qepe3 tovny A npamy b. r{epea npa*ri a i b, rqo neperuHarorbcs, npoBeAeMo trJlo-, rrlr{Hy y. I{s n:rorqnna nepe'rl4Hae o(, a or}r{e, aa AoBe,qeHIrM rreperr,ruae i F. y n ct : b, y ^ B : c, b ll c. Ilpami a,.b, c ne'. Eiarr, y nJ'roquui y i napare,rrni. flpaua a neperruae oArry g ABox [apaJreJrr,Hux npfiMrrx, a or]rie, neperrraae i Apyry a at c : B, Maeuo: trpsMa a fieperr4Hae n;rorquny I, IIIo ft rpe6a 6y;ro gorecrr, 296. Hexafr aagani Aei unmo6irxni nparri a i b, a c a, b r-, a : r{epes rouxy A n n.norqzni o npoBeAeMo npsMy c, c ll a. He' pee npnlri b i c mo:rcna eAfiHI,rM qr4HoM rrpoBecrtr nJrorqrauy F, F lL ". {epes nparry o Mo}fiHa eAr4rrr4M qI,rHoM trpoBecrrr rrJrorr{rlHy y, flapaJreJrr,r{y B. Orxce, vepea 6y4r-sxi rrrnmo- 6ixtui npsmi Mor+cua npoBecrr,r e,qrrHy rrapy [apaJreJrbHr4x nJroIqrrH, 297. fl.norquna, flrda npoBe4eua qepea r'psrwi CA i CAt, neperr.rnae u no AAr, B - no BBr i AALII BBt. Topi LACA, - ABCB, Ba .4BoMa lcyraMr.r (lC - cnintlruir, tcAA, - zcBB, I -?-4 =+ = 44 . 1ua;,aeuo,4A,: CB CB, BB, a) AC - 2 cw, AB: 6 cu, BB1 : 10 ciu, ro4i BC : AC + A' A4 AC.BBI t AB- Ba - 8 cu. :::1 ='":1. asiarcu &L = "- ;=+:;; ,*i- ','." ""^"""u BC 2BB. 2.lAzsitxu 4 =-=--:=4 (cm): v) AC : 2 cw, BBr: 8 cu, CB : AAr; + = +, AAr:4cMi ' CB BB,' r)AC:2cm, BB,:24cm, BA: AAt. Hexafi gcia AB - tccu, CB * (x+ 2)c.,i*. *,=+, 2 .=-'-"- CB BBr' x+2 x(x + 2) : 48, x2 + 2x - 48 : 0, sniAHn.r : -8 < Bi0noai0u:.a) 2,5 cw; 6) 4 clr; s) 4 cm; r) 6 cu. 298. Hexarl nprma d flepervHae n.llorutruy o n ro.rq npcnna b neperr,rHae rrJroirlr4ny o n rotqiA, fiJrorqr,ru rrpoxoArrrb uepes npsui a i b, rp neperrrHarorrrclr, rreperr,rEae nJ'rou{r4ny o'no AAr, rrJrorqr.ruy F - no BB1 i AAt ll .B.ar. To,qi AACA, - LBCB, aa ABoMa i{y- rawu (ZACA, : BCB. rn neprranan.uni, IAAC : ZCBB, ax snyrpiurri pianocroponni npz AArll BB, i civuifi,43). .AAACACOT}}ce. MaeMo: ' -::- = s. SHaiineuo AA,: BB, BC B,C a)AC:2 cvr, .BC : 5 cu, B,B : I5 cm; 49 = M=AC#, M=L#=6 ("'),BC AI- AA ' A 6)AC : BC : 2 :3, BB,:9cM, ===, : ='"'BC BBr',3 n) AC : 1 cm, BrB : 6 crvr, AA, : AB, BC : AB - A Ac=4- 1 =44- aa-"-A-4-=6- BC BB1' A,4" - 1 6 Hexaft gotxranaAA, - tc cvr, tc > 0, ro4i x2 - sc - 6 x : -2 < 0, orxce, /A, : 3 "*. r) AC :3 crra, B,B : !2 c;ln, AAr: g3' ,4,4' - 6 "*. A4 BB,, Ac _4 BC BB,, !ii t':t{.i}: Bidnoeida: a) 6 cM; 6) 6 cm; e) 3 ciu; r) 6 cnn. 299. AB ll cn, nc c a, BD c 0, cr ll B, ro,qi AB : CD rparr. Bnafigerro AD i BC - giaroirani napaJreJrorpaM a) DC : 25 c*r, AC : 7 cut, ICAD: 90', roAi AACD nnorcyrnlrft, CD - rinorenyaa, AD = tED" - Ae, AD = tE|" 1" = 24 (cM)i to =!en. Ao: L2 c.,r*. 2 Poarrsrel,ro LACO (ZOAC: 90') OC = J AC'z + eO' oc = 'liltz" = JrsS (cnr), rosi BC : 2ac, BC = 2l[93 clr. 6) AC : 5 cn, CD : 8 cu, /ACD : 12O" . Is LACD sa reopeMoro rocnnycin ADz : ACz + CD2 :illiiii:*;iiiiii# TEOMETPI9 6eas F. Il. ra ix. Ilpo904 ii:l reoMerpls EeB3 F. I'!- ra ix. IlpoQin*rrfi piBeHb i:iiiiii{iiii:fi:ii*
  26. 26. At)'=25+64-2 a t;. AD2:r2g, AD-u1729 ct.. ,flxu1o y traparlerorpaMa ABDC /ACD: L20", ro ICDB :60'' Is ABCD (BD : AA : : 5 cvt, CD:8 cu) ea reopeMolo xocunycin BC2 : BD' + aD2 - 2BD DC 'coslBDC' BC'=25+64 2 5 8'!, BC2- 49' BC - 7 cut' 2' Bilnoai}a: a) 24 cw i 2^/i93 c:u; O J72g cu i 7 cu. 3OO. y rerpae4pi,4-BCD DM = MN = NB= '!DB tpo"uoeuon'rorqrzHyANC, aHane- ;J perr Hae rpaHs BDC no CN, rpaHr'4-DB - ttSalf. Ilpone4euo s ryaui BDC MM,llCN ' M, e DC, a erpauiADB - MMrllAN, M" e ,4r. Ocrcinbriu M - cepeArrrra DN' ro M, i M, - cepegunz ni4loni4Ho DC i DA i MMr - cepeAH,fl ,risis ACDN, MM, - ce- pegHa riuia AA-DN, I1 roil MM. ='CN=1.25 12,5 (cm). 22 nru,=!dN, **,-t.25=r2,5 (cv). A Y LADC M rM, - cePegHa ,rinia i M,M- =l oc, M,M" 1-. ta = z ("*).q2 '| Pr,rr,, =7 ' 2 12'5 = 32 (cn); i Pn, ,u = l6 ciu: s*,*,,=.llEo6 lloe-z,sf , s,,,*"=f6 ,€J3 =42 (cm2). Bilnoailu: 32 cv-; 42 cxr2. 3O1 . IlponeseMo qepe: r. A' e rpaniAPC Ap, ll AC, C' e PC's rpani -A?B ArB, ll AB, B, e PB. To4i AArBrCr - iuyxauufi nepepio. Y AA?C PAt : ArA - 2 : 3, ro4i aa reoPemoo @areca PCt:CtA:2:3, AA1PC' - LAPC (lP - cnfurr'nufi, zPArC, - ,/ PAC ;t.r" si4nosiaHi nPn ArC, AC i ciunifi A?). A A-P A^C, A,P 2 "loti * = AC' , ocRlrrbKn 4= B, A-P 2 ro ' =-.AP5 Ocri:rsxu LABC - npasum'nuft, to MrBtCt - TeJfi trpaBfirbHfir4' t LAtBtCt. LABC aHoetpiuieatovnoai6Hocri k "-. 302- Ilpone4en4o n (ABC) XY ll AC, Y e BC; n (AA:B) YY. AA.,Y.e 8.C.. To4i rpamoxyrauu XXTYTY - uryrcairnii nepepia, XXt:YYl: a. XB= nV =!a.D Is LXBY (IXBY :9O") P"&, = ,(".**)= Bionoaior,: !(s*sJi). .XY = XBE,, "" =?+ !(s.s"E). 306. Hexafi,4BCDA.B)C.D. - qacrr{Ha goutcu i AAT lpaHi-4ArBrB i DDP,C Jrer+carb y naparrefibur4 x nrro Touy nronlzna (AArD) neperfiHae rx no napaleltH muxAA, i DDr. Ana;roriqnoAD ]ArDr. Orme, y qor uut<a AATD TD nporurexui cropoHz relr{arb Ha trapaJ trpsMux, rogi AATDTD - lapaJreJrorpaM. 3O9. ABDC - napaJreJrorpam, ocHi.nrxn a.ll B, AB ll C CB : 7 cm, AD - ,h2g cv, DC : AC + 3 (cu). Hexafr AC - ,r cM, BD - x cm, ro4i AB (r: + CD (r + 3) cu. Is LBAD AD2 : AB2 + BD2 - 2AB . BD . coslABD ADz : (x -f 32 'l x2 - 2x(x + 3) coslABD, 129: x2 i 6xi9i x2 2x(x+ 3)cos1A-BD, cosZAtsD 2x' + 6x - L2O . iz LBCD BC': BD' + CD' 2BD CD cosZBDC, 49: x2 + (r + 3)'z- 2x(x + 3) cos(180'- LABD), ,.o, P,rr'", = p. Pnu", -Z' ' Pou" P*" 5 sr,r,", - ,r. So,Aq, 4 s* -"' sr"" 25' Binoeilo:24 cm i 16r,8 cu'?. 906 ::i::: TEOMETPIS Eees f. fl. ra ix. flpoQinuxnft piBeHb ii{;ii:i:iliiiiiiiiiii;i;iii 2P._^ 2.3 .20 . p^ .,. = -' 4B-!- = - --" - !{ (gx{). 55 .20'rE .q = 4s*r =o' --4 - 4ooJ5 = 16J3 (cm,). 25 25 25 ' 49: v2 + x2 + 6tc. + g +3x@ i 3)cos1ABD, cos "ro..i 2*"^+6x -^l2o - o^-zx'z lu*, ,*, + 6x -' 2r(x + 3) 2x(x + 3) 4x2 +12x 160:0; i + 3x 4O: O; x : 5, x : Orxe, BD : AC : 5 cm,.4B : 8 cwr. Bi1noei1a: BD : 5 cu, /B : 8 cu. 31O. flpone4eno n rpairiADC MN I DC, N e AC,n rp Toai LMNK - r-uyxaurfi nepepi;. AMNK .! ADCB. Ocni.nrru AM : MD : 1 : 3, ro AM : AD : L: 4. Togi xoe(birlierir noAi6- _1Hocrl rp[]ryrHuxtn h = i. ^ o'JB A Src.o. 4 On, Aea-cTopoHaplBHoCTo- ponuboro LBDC, roxi ot -25! . !5' 16 _ -16 48 a --. P.-.^ '3V3 VB Vs [{ili}::r*t;t;$i{i TEOMETPI9 Eees F. Il. ra ix. l-lp
  27. 27. ls MBD (ZBAD :90") BD -- JAu AD' , BD = p*o* =ir*", = fr, o"nin * P6vNr i Paooc: k' Sourr i Saarc : h'i S*** 64=4. Bidnoeidu: cm;4 cuz, 311. no6y.qyeuo nepepio rerpae"4pa rrrlolqrrHolo (ADP)' ueft nepepia - MDP. Ilpooe- D AeMo r{epeo roury M y ',pati ADC MK ll AD' K e CD, y rpairi CDB KN ll DP, N e CB. To,4i LMKN - uyxanrii nePePia. MKMCMKl or*u ,]LCAD i o"= "c. l? =E' A **=i =5t (cm). 3a yuonoro MBC * Pinno6e4Penuft (AC : AB) i P -cepe4rana BC, 'toPi AP - rrne4iaua i nucora, CP : 8 cm. ls MPC (IAPC :90') uaeno: AP = lW - cP' , At' = lo' - g" = ar&T (cu). AcMN- rcnPi W=H H=]. ."oro =!!4 "*. ocxi.nrrcrE DC : DB, ryo LCDB - piano6e4pearafi, to4i ueAiaaa DP e i ftoro nucotoro. ts LCDP (tcPD :90') DP ='Eo" - cp'' DP = ^hr' - a' = 15 (mr)' ft'N =1. KN=lq=5 (crvr).ACKN - LCDP. roai *' , iJ 4J2r -2Bidnosidb: 5cli., cM, b - cM. 312. Ba ynonoro A'JVI : t1N, roAi MN ll Apt. Ciuna unoulrlna (MNK) neperrruae na- pa.,re.,rini rrrrolqulrn (AA.D1) i (BCC) no ilaparrerbrll4x npfiMr{x' V rpani BBtCtC npo- neger,no K? ll MN, T e BBt. MNKT - npsMotyrur'rx i uyxauuft nepqpio' MN : KT: a. B, C, flponegeuo a rpani DDTCTC qepes roq-r{rl N i K npsrri' na- pa.ne,rr'rriDC,roAiNEKF-'p"*o*y'""*iNK-iioroo,ffi.,''|u giarona,rr,. *F = ,+, *ffi" E"FR : a, "n = i? - a'. NK = i Jro r."r. P,.,", = 21a. 3'nnl = l,(s * .,{ot. 2t- Bidnoai}a: f, a(3 + V10l c:r. 313. flo6y4yeMo nrrolqrruy (BBp). Ilponegeuo n rpani A,BrCrD, MN ll BrDt, N e ArDt; r rpani AATBTB ME ll BBv E e AB; n rpani,4SCD EK ll BD, K e AD' Ilpauoxyrnnx MNKE - ulyxannfi nepepia, y fiKoro ME : NK : AAt: c. C 31 4, Ciqua nrrorqrrHa nepernnae rpaur AATBTB no AK y LABD.E,K - cepe4ra ;rinia, r:omy nX - nn, 2 ( "['-bP) /" "T^ri D -ct^L',l=2c+rla"+b..SMNKE-ME 2, Bibnoaia: z"*nE *u"; , JO:* . 2 rrlr,rHa rreperfirrae napareJrbHy rpan:o ArBrCrD, no Xn KE ll ArCu E e BrCr,.E - cepe4rana BrCr. Topi AK -yrru""ii .repepis, AI{EC - pinno6iuHa rpaneqi 3a ymoaoro AB : BC : a, rogi lC = ali, 4C, = KE - cepeAng ,rinir AArBrCr, ,o*V XA = $. flponegeuo srpar'e4iiAI{EC eracory KH, H e AC, I 16 KH LAc. Arr =AC -KE , AE = 2 E o"lid,tz - o 2 - u, 12 6 Ia MKH (1AI{K :9O') KH : AH tgtKAH, s^*={{! ru, E oJi'a.Jz + t; - , utz s*,,-----i- 4 tsa=t+ frr*=4 flxnlo o : B,z8.qM, a : 7s',nnaeuo: s -3'3'78'z- Bilnoeida: =20 Awz. 3'15. Ilo6yayeuo nepepis rcy6a n.norquHow (BMD). V rpani DD.CTC npoBeAeMo Cfi )l DM, E e DD,, E - cepeguua DDr; n rpani BBTCTC npone4euo Cf 1 FeBBr,F*cepegtnaBBr. flpama, [aparrerrr,Ha OM (O - cepe.4fiHa BD], C,A. To4i vorr,rpuxyrwraxAFCrE - myrcarruii nepepiz, A.FCT pom6, ocni.nr,r<r.r AE - ECt : FCt : AI sttt rinoreHyau nnx npsMorcyrHlrx rpzrcyruraxie M,ED, LCIED' LC, AAFB (narorr pinni ri4norigxi rcareru). :1tI.91..'"..1:.: ,if$iiiili ,il lii;i::11:::::: DA rs MED (}ADE : so") AE = JAD ED". AE = Toni P*","=^ +=zal|. s-c,,= !7,c,.rr, pe Ac!-8a2, ACr=oJs, rn=nD=ali; s*",, Bi|noeiiu: 2aJ8: o" JB 2 908 iii: TEOMETPIS 6eee F. fl. ra ix. rlpoQinuxui piBeHb i:.*;1i!ii;iiiiiii!iiii tliiiiliiilii..".*li: TEOMETPIS sees F. Il. ra in. Ilpo

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