Page 171 - Mathematics_Form_3
P. 171
Circles
P T
X
Q 3x 5x y T
144º R
FOR ONLINE READING ONLY
O P Q
O
25. In the following figure, find the Prove that:
value of x (all dimensions are in (a) ( ) ( )( )
2
centimetres) PQ = QT QX
( ) ( )( )
(b) PX 2 = QX TX
28. In the following figure,
AB BC= show that
B
2
2
8 8 OB − ( ) ( ) ( )( )
=
QC
QC PQ .
O
15
x
A O B C
A Q
P
26. The diameter AB of a circle 29. If PQR is a triangle and X is a point
with centre O is produced to T
Mathematics for Secondary Schools 27. In the following figure, PQ is the on PR such that PXR = 2PQR and
so that AB BT.=
The line TX
ˆ
ˆ
is a tangent to the circle and X is
the point of contact. Prove that
ˆ
ˆ
ˆ
ˆ
RXQ =
2XPQ. If TPQ = XRQ,
( )
( )
2
2
TX
8 OX .
=
prove that TP is a tangent to the
circle with centre at X passing
diameter of the circle with centre
O, TP is a tangent and QXT is a
secant. through P,Q , and R.
164 Student\s Book Form Three
18/09/2025 10:00:00
MATHEMATIC F3 SB.indd 164 18/09/2025 10:00:00
MATHEMATIC F3 SB.indd 164
