Question -
Answer -
The radius of the circle is
(A) 7 cm (B) 12 cm
(C) 15 cm (D) 24.5 cm
Answer:
First, draw a perpendicular from the center Oof the triangle to a point P on the circle which is touching the tangent. Thisline will be perpendicular to the tangent of the circle.
So, OP is perpendicular to PQ i.e. OP ⊥ PQ
From the above figure, it is also seen that △OPQ is a right angled triangle.
It is given that
OQ = 25 cm and PQ = 24 cm
By using Pythagoras theorem in △OPQ,
OQ2 = OP2 +PQ2
(25)2 = OP2+(24)2
OP2 = 625-576
OP2 = 49
OP = 7 cm
So, option A i.e. 7 cm is the radius of thegiven circle.