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I. (3 points)
Consider the rectangle IAHB such that IA=3 cm and IB= 5 cm. E and D are the symmetric
respectively of A and B with respect to I.
1) Construct the figure.
DI=IB=5 (sym)
IA=IE=3 (sym)
2) Correct the following statements with
justification.
a. BD=EA.
False DB=10 while AE=6
b. The triangle IAB is a right isosceles triangle
at I. F, IAB is only right triangle not iso. ( IA≠ 𝐼𝐵)
c. The quadrilateral EDAB is a square.
F, In a square the diagonal must be equal but DB≠ 𝐸𝐴 𝑝𝑎𝑟𝑡 2. 𝑎)
d. The perimeter of IAHB is equal to 8 cm.
F, P=2× 3 + 2 × 5 = 6 + 10 = 16 𝑐𝑚
e. The area of EDAB is equal to the double of IAHB.
A of EDAB =
𝐴𝐸 ×𝐷𝐵
2
=
60
2
= 30 𝑐𝑚2
but the area of IAHB=3 × 5 = 15𝑐𝑚2
𝑎𝑟𝑒𝑎 𝑜𝑓 𝐸𝐷𝐴𝐵 = 2 × 𝑎𝑟𝑒𝑎 𝑜𝑓 𝐼𝐴𝐻𝐵
II. (4 points)
Given two circles C(O;2cm) and C’(O’; 𝒙) such that: OO’=6 cm. Calculate the value(s) of
x, in each of the following cases:( x is a number strictly greater than 2 cm)
1) (C) and (C’) are tangent externally.
𝑂𝑂′
= 𝑥 + 2 𝑡ℎ𝑒𝑛 𝑥 = 6 − 2
= 4 𝑐𝑚
2) (C) and (C’) are tangent internally.
𝑂𝑂′
= 𝑥 − 2 𝑡ℎ𝑒𝑛 𝑥 = 6 + 2
= 8 𝑐𝑚
3) (C) and (C’) are interior
OO’< x-2 then 6<x-2 then x>8 cm
4) (C) and (C’) are exterior
OO’> x+2 then 6>x+2 then x<4 cm
5) (C) and (C’) are secant.:x-2<6<x+2
Grade: G8
Section: A2, B2, C2
Subject: Mathematics
Name:_________________
Abdel Karim el Khalil School
2020-2021
Date: 12-12-2020
Test: Chap2+chap4
correction
Duration: 50 min
Teacher: Zeinab zeineddine
Page 2 of 2
III. (3 points)
Let [AB] be a segment of length 5 cm.
1) Draw the circle (C) of diameter [AB]. Place O,
the center of (C).
2) What is the length of the radius r of (C)?
R=AB÷ 2 = 2.5 𝑐𝑚
3) Let E, F and G be three points such that: OE=1.5
cm; OF=2.5 and OG=3.5 cm. Plot E, F and G.
4) Indicate and justify the relative positions of the
points E, F and G with respect to (C)?
OF= 2.5= r then F on (C)
OG=3.5>r the G outside (C)
OE=1.5 < r then E inside (C)
5) What do we call [AF] with respect to (C)? what do we call [OF] with respect to (C)?
[AF] is a chord, [OF] is a radius.
6) Draw through A, a line (d) perpendicular to [OA]. What is the position of (d) with
respect to (C)? (d) is a tangent
IV. (Bonus)
Given the two circles C (O; R) and C’(O’; R’), where R=3𝑥 − 2; 𝑅′
= 2𝑥 − 4;
𝑂𝑂′
= 12 − 𝑥; and x is a measure length such that: 2 𝑐𝑚 < 𝑥 < 12 𝑐𝑚. Calculate x if these
two circles are internally tangent.
OO’=R-R’ then 12 − 𝑥 = 3𝑥 − 2 − (2𝑥 − 4)
12 − 𝑥 = 3𝑥 − 2 − 2𝑥 + 4
12− 𝑥 = 𝑥 + 2
12 − 2 = 𝑥 + 𝑥
2𝑥 = 10 𝑡ℎ𝑒𝑛 𝑥 = 5 𝑐𝑚
GOOD WORK

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Test2 circle square with the correction

  • 1. Page 1 of 2 I. (3 points) Consider the rectangle IAHB such that IA=3 cm and IB= 5 cm. E and D are the symmetric respectively of A and B with respect to I. 1) Construct the figure. DI=IB=5 (sym) IA=IE=3 (sym) 2) Correct the following statements with justification. a. BD=EA. False DB=10 while AE=6 b. The triangle IAB is a right isosceles triangle at I. F, IAB is only right triangle not iso. ( IA≠ 𝐼𝐵) c. The quadrilateral EDAB is a square. F, In a square the diagonal must be equal but DB≠ 𝐸𝐴 𝑝𝑎𝑟𝑡 2. 𝑎) d. The perimeter of IAHB is equal to 8 cm. F, P=2× 3 + 2 × 5 = 6 + 10 = 16 𝑐𝑚 e. The area of EDAB is equal to the double of IAHB. A of EDAB = 𝐴𝐸 ×𝐷𝐵 2 = 60 2 = 30 𝑐𝑚2 but the area of IAHB=3 × 5 = 15𝑐𝑚2 𝑎𝑟𝑒𝑎 𝑜𝑓 𝐸𝐷𝐴𝐵 = 2 × 𝑎𝑟𝑒𝑎 𝑜𝑓 𝐼𝐴𝐻𝐵 II. (4 points) Given two circles C(O;2cm) and C’(O’; 𝒙) such that: OO’=6 cm. Calculate the value(s) of x, in each of the following cases:( x is a number strictly greater than 2 cm) 1) (C) and (C’) are tangent externally. 𝑂𝑂′ = 𝑥 + 2 𝑡ℎ𝑒𝑛 𝑥 = 6 − 2 = 4 𝑐𝑚 2) (C) and (C’) are tangent internally. 𝑂𝑂′ = 𝑥 − 2 𝑡ℎ𝑒𝑛 𝑥 = 6 + 2 = 8 𝑐𝑚 3) (C) and (C’) are interior OO’< x-2 then 6<x-2 then x>8 cm 4) (C) and (C’) are exterior OO’> x+2 then 6>x+2 then x<4 cm 5) (C) and (C’) are secant.:x-2<6<x+2 Grade: G8 Section: A2, B2, C2 Subject: Mathematics Name:_________________ Abdel Karim el Khalil School 2020-2021 Date: 12-12-2020 Test: Chap2+chap4 correction Duration: 50 min Teacher: Zeinab zeineddine
  • 2. Page 2 of 2 III. (3 points) Let [AB] be a segment of length 5 cm. 1) Draw the circle (C) of diameter [AB]. Place O, the center of (C). 2) What is the length of the radius r of (C)? R=AB÷ 2 = 2.5 𝑐𝑚 3) Let E, F and G be three points such that: OE=1.5 cm; OF=2.5 and OG=3.5 cm. Plot E, F and G. 4) Indicate and justify the relative positions of the points E, F and G with respect to (C)? OF= 2.5= r then F on (C) OG=3.5>r the G outside (C) OE=1.5 < r then E inside (C) 5) What do we call [AF] with respect to (C)? what do we call [OF] with respect to (C)? [AF] is a chord, [OF] is a radius. 6) Draw through A, a line (d) perpendicular to [OA]. What is the position of (d) with respect to (C)? (d) is a tangent IV. (Bonus) Given the two circles C (O; R) and C’(O’; R’), where R=3𝑥 − 2; 𝑅′ = 2𝑥 − 4; 𝑂𝑂′ = 12 − 𝑥; and x is a measure length such that: 2 𝑐𝑚 < 𝑥 < 12 𝑐𝑚. Calculate x if these two circles are internally tangent. OO’=R-R’ then 12 − 𝑥 = 3𝑥 − 2 − (2𝑥 − 4) 12 − 𝑥 = 3𝑥 − 2 − 2𝑥 + 4 12− 𝑥 = 𝑥 + 2 12 − 2 = 𝑥 + 𝑥 2𝑥 = 10 𝑡ℎ𝑒𝑛 𝑥 = 5 𝑐𝑚 GOOD WORK