Question

15. In figure, O is the centre of the circle. PQ is a tangent
to the circle and secant PAB passes through the centre
O. If PQ = 5 cm and PA = 1 cm, then find the radius
of the circle
5 cm
P.
1 cm A​

Answer 1

In Circle with centre O ,
AO or OQ or OB all are radius

Let the radius of circle be ‘x’

AO=OQ=x

As Angle Q is 90 degree
So, Triangle PQO is Right angled triangle

Side PO = PA + AO
= 1 + x
Therefore, By Pythagoras theorem
PO^2 = OQ^2+ PQ^2
( 1 + x ) = x^2 + 5^2
1 + x^2 + 2x = x^2 + 25 ( Subtracting x^2 from both side )
1 + 2x = 25
2x =25 - 1
2x = 24
x = 12

There fore measure of radius of circle is 12 cm

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