Test 2 circle and square with 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