Page 166 - Mathematics_Form_3

Circles

12. The chord AB of a circle with
centre O is produced to T such
that AB BT.= A tangent TX is
drawn to the circle. Prove that
30º
FOR ONLINE READING ONLY
( ) 2 = 2 AB .
( )
2
TX
13. In the following figure, TA is
a tangent to the circle centred
Find the size of each of the at O. If OX is perpendicular
following angles: to the secant PQT, prove that
̂ ̂ ̂ 2 2
(a) P O T (b) O R T (c) R T Q ( ) ( ) = TQ TP.×
OA
OT −
9. In the following figure, find the P

sizes of the angles marked x and y. X
Q
P
O
y T
40º N
Q x

A
M
Chapter summary
10. In the following figure, calculate 1. If an arc subtends an angle x at the
TA , leaving your answer in radical centre of a circle of radius r, then
form. its length is x × 2 r orπ π rx .

A 360° 180°
2. If r is a radius of a circle and AB is
an arc of length l, then the ratio
l _
r
is the angle at the centre of the
3 cm 9 cm
X Y T circle in radians. Mathematics for Secondary Schools
3. To convert an angle from degrees
11. Two chords PQ and RS intersect into radians, multiply the given
externally at T, and TX is a tangent π
, which is about
angle by ____
to the circle, X being the point of 180°
contact. If PQ 8cm,= RS 3cm,= 0.01745 radians. To convert an
and ST 12cm,= 45 cm, calculate QT angle in radians into degrees,
180°
____
and TX (leave your answer in multiply the given angle by π ,
surd form). which is about 57.3 ° .

Student\s Book Form Three 159

18/09/2025 09:59:56
MATHEMATIC F3 SB.indd 159
MATHEMATIC F3 SB.indd 159 18/09/2025 09:59:56