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I. (3 points)
Answer by true or False with justification:
1) The greater chord of a circle is the radius.
2) If OA= 5 cm, the point A is outside the circle C(O; 5 cm).
3) A line at a distance 6 cm from the center of a circle of radius 7 cm
intersects the circle in two distinct points.
4) The center of a circle can be determined by the intersection of two
perpendicular bisectors of any two of its chords.
5) If OB= 4 cm then the point B is outside the circle C( O; 3 cm).
6) The circles C(O; 4 cm) and C’(O; 4 cm) such that OO’=8cm are
tangent internally.
II. (4 points)
C(O; R) and C’(O’;R’) designate two circles. How would you choose:
1) R’ so that the two circles are externally disjoint, knowing that OO’= 6
cm and R=4.5 cm?
2) R’ so that the two circles are internally disjoint, knowing that OO’= 5
cm and
R= 3 cm.
3) OO’ so that the two circles are intersecting, knowing that R= 3 cm and
R’= 5 cm?
4) R and R’ so that the two circles are externally tangent, knowing that
OO’=12cm and R is the triple of R’?
5) Given (C ) and (C’) are externally tangent circles, where: OO’= 15
cm. Calculate R and R’, if R’ exceeds R by 3 cm.
6) Given the two circles (C ) and (C’) are internally tangent, and OO’= 9
cm. Calculate R’, if R is twice the radius of (C’) decreased by 3 cm.
Grade: 8 A, B, C
Subject: Mathematics
Name:_________________
Abdel Karim el Khalil School
2020-2021
Date: 4 Dec 2020
Test 1
Teacher: ZeinabZeineddine
Page 2 of 2
III. (5 points)
Let [AB] be a segment of length 5 cm.
1) Draw a circle (C) of center A and radius R= 3 cm, and a circle (C’) of
center B and radius R’=2 cm.
2) Justify That (C) and (C’)are externally tangent.
3) Let I be the point of tangency of (C) and (C’). draw through I, a line
(d) that intersects (C) and (C’)at M and N respectively.
Show that AMI and BNI are two isosceles triangles.
V. (3 points)
ABC is a right triangle at A such that AB = 2 cm and AC = 4 cm. I is
the midpoint of [AC], M and N are the symmetric respectively of B
and I with respect to the point A.
a) Draw the figure.
b) What is the nature of MNBI? Justify.
GOOD WORK

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Test 1 square circle

  • 1. Page 1 of 2 I. (3 points) Answer by true or False with justification: 1) The greater chord of a circle is the radius. 2) If OA= 5 cm, the point A is outside the circle C(O; 5 cm). 3) A line at a distance 6 cm from the center of a circle of radius 7 cm intersects the circle in two distinct points. 4) The center of a circle can be determined by the intersection of two perpendicular bisectors of any two of its chords. 5) If OB= 4 cm then the point B is outside the circle C( O; 3 cm). 6) The circles C(O; 4 cm) and C’(O; 4 cm) such that OO’=8cm are tangent internally. II. (4 points) C(O; R) and C’(O’;R’) designate two circles. How would you choose: 1) R’ so that the two circles are externally disjoint, knowing that OO’= 6 cm and R=4.5 cm? 2) R’ so that the two circles are internally disjoint, knowing that OO’= 5 cm and R= 3 cm. 3) OO’ so that the two circles are intersecting, knowing that R= 3 cm and R’= 5 cm? 4) R and R’ so that the two circles are externally tangent, knowing that OO’=12cm and R is the triple of R’? 5) Given (C ) and (C’) are externally tangent circles, where: OO’= 15 cm. Calculate R and R’, if R’ exceeds R by 3 cm. 6) Given the two circles (C ) and (C’) are internally tangent, and OO’= 9 cm. Calculate R’, if R is twice the radius of (C’) decreased by 3 cm. Grade: 8 A, B, C Subject: Mathematics Name:_________________ Abdel Karim el Khalil School 2020-2021 Date: 4 Dec 2020 Test 1 Teacher: ZeinabZeineddine
  • 2. Page 2 of 2 III. (5 points) Let [AB] be a segment of length 5 cm. 1) Draw a circle (C) of center A and radius R= 3 cm, and a circle (C’) of center B and radius R’=2 cm. 2) Justify That (C) and (C’)are externally tangent. 3) Let I be the point of tangency of (C) and (C’). draw through I, a line (d) that intersects (C) and (C’)at M and N respectively. Show that AMI and BNI are two isosceles triangles. V. (3 points) ABC is a right triangle at A such that AB = 2 cm and AC = 4 cm. I is the midpoint of [AC], M and N are the symmetric respectively of B and I with respect to the point A. a) Draw the figure. b) What is the nature of MNBI? Justify. GOOD WORK