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Circle Review Class
- 1. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
वृत्त
Circle
Facilitated by : Bijendra Bir Karmacharya
for
Virtual Classes for SEE students
Presented by
Bhaktapur Municipality
2077 Baishakh
गणित (Mathematics) >> ज्यामितत (Geometry) >>
- 2. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Questions and Total Marks from Circle
Group A 1 × 1 = 1
Group B 2 × 2 = 4
Group C 1 × 4 = 4
Group D 1 × 5 = 5
Total Q = 5, Marks = 14
- 4. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Group A Questions from Circle
Each of 1 Mark
No. of questions from Circle: 1
Q.No. 3b
- 5. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A1. सम्िुख चापहरू बराबर हुने के न्द्रीय कोिहरूको सम्बन्द्ध लेख्नुहोस् ।
Write the relation between central angles having equal opposite arcs.
सम्िुख चापहरू बराबर हुने के न्द्रीय कोिहरू बराबर हुन्द्छन् ।
The central angles, having equal opposite arcs, are equal.
- 6. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A2. के न्द्रववन्द्दु O भएको एउटा वृत्तिा ∠AOB = ∠COD छ भने चाप AB र चाप CD ववचको
सम्बन्द्ध लेख्नुहोस् ।
In a circle with centre O, ∠AOB = ∠COD. State the relation between arc AB and arc CD.
बराबर के न्द्रीय कोिहरूका सम्िुख चापहरू पतन बराबर हुन्द्छन् ।
अतः चाप AB = चाप CD हुन्द्छ ।
Opposite arcs of equal central angles are also equal. So, Arc AB = Arc CD.
- 7. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A3. एउटा वृत्तको के न्द्रववन्द्दु O छ र चाप AB र चाप CD दुई बराबर चापहरू हुन् भने जीवाहरू
AB र CD ववचको सम्बन्द्ध लेख्नुहोस् ।
O is the centre of a circle and two arcs arc AB and arc CD are equal arcs. What would
be the relation between the chords AB and CD ?
बराबर चापहरूले बनाउने जीवाहरू AB र CD बराबर हुन्द्छन ् । अतः AB = CD ।
Chords AB and CD subtended by equal arcs are also equal. i.e. AB = CD.
- 8. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A4. के न्द्रववन्द्दु O सहहतको एउटा वृत्तिा क्रिशः A, B र C ततनवटा ववन्द्दुहरू चचत्रिा जस्तै
पररचधिा छन् भने ∠AOB र ∠ACB ववचको सम्बन्द्ध लेख्नुहोस् ।
In a circle with centre O, there are three points A, B and C on the circumference
given as in figure. State the relation between the angles ∠AOB and ∠ACB.
के न्द्रीय कोि पररचध कोिको दोब्बर हुन्द्छ । अतः ∠AOB = 2∠ACB हुन्द्छ ।
The central angle is double of the inscribed angle . i.e. ∠AOB = 2∠ACB.
- 9. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A5. एउटै चापिा आधाररत के न्द्रीय कोि र पररचध कोि ववचको सम्बन्द्ध लेख्नुहोस् ।
State the relation between the inscribed angle and central angle standing in same arc.
एउटै चापिा आधाररत के न्द्रीय कोि पररचध कोिको दोब्बर हुन्द्छ ।
The central angle is double of inscribed angle standing in same arc.
- 10. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A6. ABCD एउटा चक्रक्रय चतुभुुज हो भने ∠BAD र ∠BCD ववचको सम्बन्द्ध लेख्नुहोस् ।
ABCD is a cyclic quadrilateral. State the relation between ∠BAD and ∠BCD.
चक्रीय चतुभुुजका सम्िुख कोिहरू पररपूरक हुन्द्छन् । अतः ∠BAD + ∠BCD = 180° हुन्द्छ ।
The opposite angles of a cyclic angles are supplementary. i.e. ∠BAD + ∠BCD = 180°.
- 11. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A7. एउटा वृत्तको पररचधिा कु नै ववन्द्दु P छ र यसको एउटा व्यास AB छ । ∠APB को िान
कतत होला ?
P is any point on circumference of a circle. AB is diameter. What is the value of angle
∠APB ?
अधुवृत्तको कोि सिकोि हुन्द्छ । अतः ∠APB = 90° हुन्द्छ ।
An angle in semi circle is right angle. So, ∠APB = 90°.
- 12. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A8. एउटा वृत्तको पररचधिा कु नै ववन्द्दु P छ र यसको एउटा व्यास AB छ भने भुजाहरू AP र
PB ववचको सम्बन्द्ध लेख्नुहोस् ।
P is any point on a circle. AB is diameter. Write down the relation between the sides
AP and PB.
अधुवृत्तको कोि सिकोि हुन्द्छ । अतः AP PB हुन्द्छ ।
An angle in semi circle is right angle. So, AP PB.
- 13. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A9. ABCD एउटा चक्रक्रय चतुभुुज हो र भुजा AB लाई बाहहर E सम्ि लम्ब्याइएको छ ।
∠EBC र ∠ADC ववचको सम्बन्द्ध के होला? लेख्नुहोस् ।
ABCD is a cyclic quadrilateral. The side AB is produced outside up to E. State the
relation between ∠EBC and ∠ADC.
चक्रीय चतुभुुजको कोि सम्िुख कोिको वाह्यकोि संग बराबर हुन्द्छ ।
अतः ∠EBC = ∠ADC हुन्द्छ ।
An angle of cyclic quadrilateral is equal to its opposite exterior angle.
So, ∠EBC = ∠ADC.
- 14. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A10. के न्द्रववन्द्दु O भएको वृत्तिा एउटा स्पशुरेखा TN छ । यहद स्पशुववन्द्दु A हो भने OA र
TN ववचको सम्बन्द्ध के होला ? लेख्नुहोस् ।
A line TN is tangent to a circle with centre O. If the point of tangency is at A, write
the relation between OA and TN.
वृत्तको स्पशु रेखा स्पशु ववन्द्दुिा णखंचचएको अधुव्यास संग लम्ब हुन्द्छ ।
त्यसैले, OA TN हुन्द्छ ।
Tangent to the circle is perpendicular to the radius drawn at the point of tangency.
So, OA TN.
- 15. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
A11. के न्द्रववन्द्दु O भएको वृत्तिा एउटा स्पशुरेखा TN छ । यहद स्पशुववन्द्दु A हो भने ∠NAO
को िान कतत होला ? पत्ता लगाउनुहोस् ।
A line TN is tangent to a circle with centre O. If the point of tangency is at A, then
find out value of ∠NAO.
वृत्तको स्पशु रेखा स्पशु ववन्द्दुिा णखंचचएको अधुव्यास संग लम्ब हुन्द्छ ।
त्यसैले, ∠NAO = 90° हुन्द्छ ।
Tangent to the circle is perpendicular to the radius drawn at the point of tangency.
So, ∠NAO = 90°.
- 16. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Group B Questions from Circle
Each of 2 marks
Total No. of questions from circle: 2
Q.No. 8b
Q.No. 8c (From Tangents)
- 17. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
B1. हदइएको चचत्रिा वृत्तको के न्द्रववन्द्दु O छ । यहद PQ व्यास र
PR = QR छ भने ∠PQR को नाप कतत होला ?
O is the centre of the circle. If PQ is diameter and PR = QR,
then find the value of ∠PQR.
?
Solution:
Here,
i) ∠R = 90° [∵अधुवृत्तको ∠ ]
[∵ ∠ in a semi circle]
ii) ∠P = ∠Q [∵ PR = QR]
iii) ∠P + ∠Q + ∠R = 180° [∵ ΔPQR का मभत्री ∠हरू]
or, ∠Q + ∠Q + 90° = 180° [∵ interior ∠s of a ΔPQR]
or, 2 ∠Q = 180° – 90°
or, 2 ∠Q = 90°
or, ∠Q = 90°/2
∴ ∠PQR = 45° Ans.
- 18. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Hints:
i) ∠BCA = …… [∵ चाप ABिा आधाररत के न्द्रीय र पररचध ∠हरू]
[∵ Central and insc. ∠s standing on Arc AB.]
ii) ∠OAC = …… [∵ समद्विवाहु ΔOAC का आधार ∠ हरू ]
[∵ Base ∠s of isos. ΔOAC ]
B2. एउटा वृत्तिा के न्द्रववन्द्दु O, व्यास BC र कु नै ववन्द्दु A छ ।
यहद ∠BOA = 70° छ भने ∠OAC को नाप पत्ता लगाउनुहोस्
।
In a circle , O is the centre, BC is a diameter and A is any
point. If ∠BOA = 70°, calculate value of ∠OAC.
- 19. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Hints:
i) ∠ADB = …… [∵ चाप ABिा आधाररत पररचध ∠हरू ]
[∵ insc. ∠s standing on arc AB) ]
ii) ∠DAB = …… [∵ अधुवृत्तको ∠ ]
[∵ ∠ in a semi circle ]
iii) …… + ……+ …… = 180° [∵ ΔDAB का मभत्री ∠हरू ]
[∵ interior ∠s of ΔDAB ]
……
∴ ∠DAB = ……
B3. हदइएको चचत्रिा BD वृत्तको व्यास हो र ∠ACB = 35° भए
∠DBA को िान कतत होला ?
In the given figure, BD is a diameter of the circle and
∠ACB = 35°. What is the value of ∠DBA?
- 20. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Hints:
i) ∠R = …… [∵ …………………………………]
ii) x + …… + …… = …… [∵ΔPQR का मभत्री ∠हरू]
[∵ int. ∠s of ΔPQR]
……
x = ……
B4. हदइएको अधुवृत्ताकार चचत्रिा x को नाप पत्तालगाउनुहोस् ।
Find the value of x in the given semi-circular figure.
- 21. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
B5. चचत्रिा के न्द्रववन्द्दु O भएको वृत्तको व्यास AB हो र
∠BOD = 150° छ भने ∠DCA को िान कतत होला,
पत्तालगाउनुहोस् ।
In the figure, AB is the diameter of a circle with
centre O. If ∠BOD = 150°, calculate the measure of
∠DCA.
Hints:
i) ∠DOA + …… = 180° [∵ सरल रेखाका आसन्द्न ∠हरू ]
∴ ∠DOA = …… [∵ Adjacent ∠s of straight line]
ii) ∠DCA = …… [∵ चाप AD िा आधाररत के न्द्रीय र पररचध ∠हरू ]
[∵ Central and insc. ∠s standing on arc AD]
- 22. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
B6. चचत्रिा PQ = PS र ∠QRS = 110° छन् भने ∠PQS को नाप
कतत होला ?
In the figure PQ = PS, and ∠QRS = 110°. Calculate
measure of ∠PQS.
Hints:
i) ∠PSQ = ∠PQS [∵ ……………………………………..]
ii) ∠QPS + …… = 180° [∵ चक्रक्रय चतुभुुज PQRS का सम्िुख ∠हरू]
[∵ Opp. ∠s of cyclic quad. PQRS]
∴ ∠QPS = ……
iii) ∠PSQ + ∠PQS + ∠QPS = 180° [∵……………………………………..]
……
∴ ∠PQS = ……
- 23. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
B7. हदइएको चचत्रिा ABCD एउटा चक्रक्रय चतुभुुज हो, जसिा
भुजा DC वृत्तको के न्द्रववन्द्दु O बाट गएको छ । यहद ∠ACD
= 40° भए ∠ADC र ∠ABC को नाप पत्तालगाउनुहोस् । In the
figure given, ABCD is a cyclic quadrilateral, in which side
DC passes through centre O of the circle. If ∠ACD = 40°,
find the measure of ∠ADC and ∠ABC.
Hints:
i) ∠DAC = …… [∵……………………………………..]
ii) ∠DAC + …… + …… = 180° [∵Δ ADC ………………………..]
……
∴ ∠ADC = ……
iii) ∠ABC + ∠ADC = …… [∵……………………………………..]
∴ ∠ABC = ……
- 24. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
B8. के न्द्रववन्द्दु O भएको वृत्तिा एउटा स्पशुरेखा TN छ
। यहद स्पशुववन्द्दु A हो र OA = NA छ भने
∠ONA को नाप कतत होला ? पत्ता लगाउनुहोस् ।
A line TN is tangent to a circle with centre O. If
the point of tangency is at A, and OA = NA then
find out measure of ∠ONA.
Hints:
i) ∠OAN = ….. [∵स्पशु रेखा र अधुव्यासको सम्बन्द्ध]
[∵Reln betn Tangent and Radius]
ii) ∠NOA = ∠ONA [∵……………………………………..]
iii) …… + …… + …… = 180° [∵ΔOAN ………………………..…]
…
∴ ∠ONA = ……
- 25. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
B9. चचत्रिा वृत्तको के न्द्रववन्द्दु O छ, रेखाखण्ड PQ ले
वृत्तलाई A िा स्पशु गरेको छ र ∠BAQ = 50° भने
∠ABO को िान कतत होला ?
In figure, O is the centre of the circle, segment PQ is
tangent to the circle at A and ∠BAQ = 50°. Now
calculate value of ∠ABO.
Hints:
i) ∠OAQ = …… [∵……………………………………..]
ii) …… + …… = …… [∵मसंगोटुक्रे तथ्य Whole Part Axiom]
∴ ∠OAB = ……
iii) ∠ABO = …… [∵सिद्वववाहु ΔOAB का आधार ∠हरू]
[∵ Base ∠s of isos. ΔOAB]
∴ ∠ABO = ……
- 26. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
B10. चचत्रिा O वृत्तको के न्द्रववन्द्दु हो र AB स्पशु रेखाखण्ड हो
। यहद CA = 12 cm र AB = 24 cm छ भने वृत्तको
अधुव्यास कतत होला ?
In figure, O is the centre of the circle , AB is tangent
segment. If CA = 12 cm and AB = 24 cm, then
calculate the radius of the circle.
Hints:
Let OB = r, so OC = r
i) ∠OBA = …… [∵……………………………………..]
ii) OA = 12 + r [∵……………………………………..]
iii) (12 + r)² = 24² + r² [∵ΔOBA िा पाइथागोरस सुत्र]
[∵ Pythagoras Formula in ΔOBA]
……
∴ r = ……
r
r
- 27. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Group C Questions form Circle
Each of 4 marks
Total No. of Questions from circle: 1
Q.No. 18
(Experimental Verifications)
- 28. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
C1. कु नै वृत्तको एउटै चाप MN िा आधाररत के न्द्रीय
कोि MON पररचध कोि MSN को दोब्बर हुन्द्छ
भतन प्रयोगद्वारा पररक्षि गनुुहोस ् । (कम्तीिा 3
cm अधुव्यास भएका दुईवटा वृत्तहरू आवश्यक छन्
।)
Verify experimentally that the central angle
MON is double of the inscribed angle MSN
standing on the same arc MN of a circle. (Two
circles having radii at least 3 cm are necessary.)
Fig No. ∠MON ∠MSN Remarks
तनश्कर्ुः यसरी वृत्तको एउटै चाप MN िा आधाररत के न्द्रीय कोि MON पररचध कोि MSN को
दोब्बर हुन्द्छ भतन प्रयोगद्वारा पुष्टट गररयो ।
Conclusion: Hence it is verified experimentally that the central angle MON is double of the
circumference angle MSN standing on the same arc MN of the circle.
Fig (i) Fig (ii)
i) 80° 40° ∠MON = 2 ∠MSN
ii) 120° 60° ∠MON = 2 ∠MSN
- 29. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
C2. कु नै वृत्तको एउटै चाप SR िा आधाररत दुई
पररचध कोिहरू SPR र कोि SQR बराबर हुन्द्छन्
भतन प्रयोगद्वारा पुष्टट गनुुहोस ् । (कम्तीिा 3
cm अधुव्यास भएका दुईवटा वृत्तहरू आवश्यक
छन् ।)
Verify experimentally that the inscribed angles
SPR and angle SQR standing on the same arc SR
of a circle are equal. (Two circles having radii at
least 3 cm are necessary.)
Fig No. ∠SPR ∠SQR Remarks
तनश्कर्ुः यसरी वृत्तको एउटै चाप SR िा आधाररत दुई पररचध कोिहरू SPR र कोि
SQR बराबर हुन्द्छन् भतन प्रयोगद्वारा पुष्टट गररयो ।
Conclusion: Hence it is verified experimentally that the inscribed angles SPR and
angle SQR standing on the same arc SR of a circle are equal.
Fig (i) Fig (ii)
i) 60° 60° ∠SPR = ∠SQR
ii) 50° 50° ∠SPR = ∠SQR
- 30. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
C3. चक्रक्रय चतुभुुज CEDA का सम्िुख कोिहरू
पररपूरक हुन्द्छन ् भतन प्रयोगद्वारा पुष्टट गनुुहोस्
। (कम्तीिा 3 cm अधुव्यास भएका दुईवटा
वृत्तहरू आवश्यक छन ् ।)
Verify experimentally that the opposite angles
of cyclic quadrilateral CEDA are supplementary.
(Two circles having radii at least 3 cm are
necessary.)
Fig. No. ∠CED ∠EDA ∠DAC ∠ACE Remarks
तनश्कर्ुः यसरी चक्रक्रय चतुभुुज CEDA का सम्िुख कोिहरू पररपूरक हुन्द्छन् भतन
प्रयोगद्वारा पुष्टट गररयो ।
Conclusion: Hence it is verified experimentally that the opposite angles of cyclic
quadrilateral CEDA are supplementary.
Fig (i) Fig (ii)
i) 70° 120° 110° 60° ∠CED + ∠DAC = 180°
∠EDA + ∠ACE = 180°
ii) 80° 95° 100° 85° ∠CED + ∠DAC = 180°
∠EDA + ∠ACE = 180°
- 31. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
C4. चक्रक्रय चतुभुुज KHWP को भुजा KH लम्ब्याएर M सम्ि पु-
याइएको छ । अब, चक्रक्रय चतुभुुजको मभत्री कोि KPW
यसको सम्िुख वाह्य कोि WHM संग बराबर हुन्द्छ भतन
प्रयोगद्वारा पुष्टट गनुुहोस ् । (कम्तीिा 3 cm अधुव्यास
भएका दुईवटा वृत्तहरू आवश्यक छन् ।)
A side KH of a cyclic quadrilateral KHWP is produced
outside up to M. Verify experimentally that the interior
angle KPW is equal to opposite exterior angle WHM. (Two
circles having radii at least 3 cm are necessary.)
Fig No. ∠KPW ∠WHM Remarks
तनश्कर्ुः यसरी चक्रक्रय चतुभुुजको मभत्री कोि KPW यसको सम्िुख वाह्य कोि
WHM संग बराबर हुन्द्छ भतन प्रयोगद्वारा पुष्टट गररयो ।
Conclusion: Hence it is verified experimentally that the interior angle KPW is
equal to opposite exterior angle WHM.
Fig (i) Fig (ii)
i) 95° 95° ∠KPW = ∠WHM
ii) 80° 80° ∠KPW = ∠WHM
- 32. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
Group D Questions from Circle
Each of 5 Marks
No. of questions from Circle: 1
Q.No. 24
- 33. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
D1. हदइएको चचत्रिा PQ // AB भए AY = BY हुन्द्छ भनी प्रिाणित
गनुुहोस ् ।
In the given figure, PQ // AB. Prove that AY = BY.
Hints:
Construction: Join X and C
1) ∠QPX = ∠BAX
2) ∠BAX = ∠BCX
3) ∠QPX = ∠BCX
4) PQXC एउटा चक्रीय चतुभुुज (cyclic quadrilateral) हो ।
5) ∠QXP = ∠QCP
6) Arc AY = arc BY
7) AY = BY
Q.E.D.
- 34. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
D2. हदइएको चचत्रिा ABC एउटा सिबाहु त्रत्रभुज हो । चाप AB
र चाप AC का िध्यववन्द्दुहरू क्रिशः D र E छन् भने XY
= 1/3 DE हुन्द्छ भनी प्रिाणित गनुुहोस् ।
In the given figure, ABC is an equilateral triangle. The
points D and E are midpoints of arc AB and arc AC
respectively. Prove that XY = 1/3 DE.
Hints:
Construction: Join AD and AE.
1) arc ADB = arc AEC
2) arc AD = arc BD = arc AE = arc CE
3) ∠AED = ∠EAC = ∠ADE = ∠DAB
4) i) AX = DX
ii) AY = YE
5) i) ∠AXY = ∠DAB + ∠ADE
ii) ∠AYX = ∠EAC + ∠AED
6) ∠AXY = ∠AYX
7) ΔAXY एउटा सिबाहु (equilateral) Δ हो ।
8) AX = AY = XY
9) DX = XY = YE
10) XY = 1/3 DE Q.E.D.
- 35. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
D3. चचत्रिा ABCD एउटा चक्रीय चतुभुुज हो र जीवाहरू AD र
BC बराबर छन् । त्रत्रभुज ADC र त्रत्रभुज BDC हरूको
क्षेत्रफल बराबर छ भतन प्रिाणित गनुुहोस् ।
In figure, ABCD is a cyclic quadrilateral and chords AD
and BC are equal. Prove that the areas of triangle ADC
and triangle BDC are equal.
Hints:
1) arc AD = arc BC
2) ∠ACD = ∠BDC
3) ∠ACD = ∠ABD
4) ∠BDC = ∠ABD
5) AB // DC
6) A(ΔADC) = A(ΔBDC) Q.E.D.
- 36. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
D4. हदइएको चचत्रिा, वृत्तको के न्द्र ववन्द्दु O हो, AB
व्यास हो र DO रेखाखण्ड व्यास AB िा लम्ब छ
भने ∠AEC = ∠ODA छ भतन प्रिाणित गनुुहोस् ।
In the given figure, O is the centre of circle, AB
is diameter and DO is perpendicular to AB.
Prove that ∠AEC = ∠ODA.
Hints:
i) यी तनला त्रत्रभुजहरूका सबै कोिहरू बराबर छन् ।
All angles are equal in these two blue triangles.
ii) र, यी पररचध कोिहरू पतन बराबर छन् ।
And these inscribed angles are equal.
अब हाम्रो तनश्कर्ु आउँछ।
So we get the result.
- 37. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
D5. हदइएको वृत्तिा दुई बराबर जीवाहरू AB र CD लाई
लम्ब्याउँदा E िा काहटएका छन । अब, BE र DE
बराबर छन् भतन प्रिाणित गनुुहोस् ।
If two equal chords AB and CD of the given circle
are produced to meet at E, then prove that BE
and DE are equal.
Hints: Join AC.
i) यी दुई राता चापहरू बराबर छन् ।
These two RED arcs are equal.
ii) दुबैिा हररयो चाप BD जोडौं ।
Add this GREEN arc BD to both.
iii) हािीले यी नीला खष्टटएका बराबर चापहरू पाउँछौं ।
We get these blue overlapping equal arcs.
iv) जसले यी बराबर पररचध कोिहरू बनाउँछन् ।
Which subtends these equal inscribed angles.
v) यसले त्रत्रभुज AEC सिद्वववाहु त्रत्रभुज बन्द्छ ।
It makes Triangle AEC an isosceles triangle.
vi) AE = CE दुबैिा AB र CD घटाऔं ।
Subtract AB and CD from AE = CE.
- 38. Circle Virtual Review Class © Bijendra Bir Karmacharya 2020
धन्द्यवाद !
ववजेन्द्रवीर किाुचायु
श्री चक्रे श्वर िा.वव., बेथानचोक-१, काभ्रे
9841271567
veejayandra@gmail.com
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