(A) 7 cm

(B) 12 cm

(C) 15 cm

(D) 24.5 cm

Answer:

First draw a perpendicular from the triangle’s centre O to a point P on the circle that touches the tangent. This line will be perpendicular to the circle’s tangent.

As a result, OP is perpendicular to PQ i.e. OP ⊥ PQ

It can also be observed in the above figure that △OPQ is a right angled triangle.

It is provided that

PQ = 24 cm and OQ = 25 cm

Using the Pythagoras theorem in △OPQ,

OQ² = OP² +PQ²

(25)² = OP²+(24)²

OP² = 625-576

OP² = 49

OP = 7 cm

As a result, option A is correct i.e. 7 cm is the given circle’s radius.