(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.