Question -
Answer -
┬аThe radius of the circle is
(A) 7 cm┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а┬а(B) 12 cm
(C) 15 cm┬а ┬а ┬а ┬а ┬а ┬а ┬а ┬а┬а(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 тКе PQ
From the above figure, it is also seen that тЦ│OPQ is a right angled triangle.
It is given that
OQ = 25 cm and PQ = 24 cm
By using Pythagoras theorem in тЦ│OPQ,
OQ2┬а= OP2┬а+PQ2
(25)2┬а= OP2+(24)2
OP2┬а= 625-576
OP2┬а= 49
OP = 7 cm
So, option A i.e. 7 cm is the radius of thegiven circle.