Page 169 - Mathematics_Form_3

Circles

A
9. In the following figure, PR and QR
are straight lines. If ‾ XR = ‾ YR,
prove that:
( a ) ‾ PQ ∥ ‾ XY O
FOR ONLINE READING ONLY
(b) ‾ PX = ‾ QY 140º
B
(c) ‾ SX = ‾ SY
D
C
Q
Y P
13. Find the value of x in each of the
S R following figures. All measurements

are in centimetres, and O is the
P X centre of the circles.

10. In the following figure, (a) R
̂
arc AB = arc CD and C X D = 130° . 8
̂
Calculate A C X and prove that ‾ AC 3 S
is parallel to ‾ BD . O
4
C Q
D P x
130º (b)

2 R
P Q
X B x O 3
Mathematics for Secondary Schools 11. Points A, B, C and D are concyclic (c) C

A

and arc AB = arc BC = arc CD.
̂
If B D C = 45° , prove that ABCD
is a square.
12. In the following figure, O is the
centre of the circle. The angle
x
subtended by arc BCD at the centre A 12 cm 10 cm
is 140°. If ‾ BC is extended to P, 6 cm B
̂
̂
determine B A D and D C P.
D

162 Student\s Book Form Three

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