Page 170 - Mathematics_Form_3

Circles

14. A circle has a centre at C and radius (c)
10 cm. If ‾ AB is a chord for which
∠ACB is 140 °, find the length of

chord AB. O
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15. The radii of two concentric circles
are 17 cm and 10 cm. A straight A x B
line ABCD crosses one circle at 120º
A and D, and the other circle at B
and C. If ‾ BC = 12 cm, calculate C
the length of ‾ AB . 19. Two tangents from point T touch
16. A tangent from an external point the circle at A and B. If TA 9cm=
T to a circle of radius 4.5 cm is and ATB 52 ,∠ = ° find ‾ AB .
16 cm long. Find the distance
from T to the nearest point on the 20. PQRS is a cyclic quadrilateral with
circumference. ∠PQR = 112 ° . Find ∠PSR.

17. If ‾ AC is a diameter of the circle 21. A point T is 6 cm from the centre
̂
̂
ABCD and B D C = 25°, find A C B. C of a circle of radius 3 cm. Find;
18. In each of the following figures, (a) the length of the tangent from
find the value of x if O is the centre T to the circle.
of each circle. (b) the angle between the tangent
and ‾ TC .
(a)
22. If C is the centre of a circle and

x AB is a chord, CAB 50∠ = ° , and
AC 6cm,= find:
O C
A D 40º (a) The length of ‾ AB .
(b) The distance of ‾ AB from C.

B
23. Let the chord PQ of a circle be
(b) Mathematics for Secondary Schools
P extended to R and ‾ RT be a tangent.
Q ̂
40º If ‾ TQ = ‾ QR, and Q R T = 35°,
2x ̂ ̂
calculate P Q T and P T Q.
O
24. In the following figure, O is the
R
x centre of the circle. Find the values
ˆ
of x and y, hence find PRQ and
ˆ
S PTR .

Student\s Book Form Three 163

18/09/2025 09:59:58
MATHEMATIC F3 SB.indd 163
MATHEMATIC F3 SB.indd 163 18/09/2025 09:59:58