Question

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of circle is

(A) 7 cm

(B) 12 cm

(C) 15 cm

(D) 24 cm

Answer 1

Correct option is (A) 7 cm

In \(\triangle OP Q,\)

\(OQ^2 = OP^2 + PQ^2\)

⇒ \(25^2 = 24^2 + r^2\)

⇒ \(r^2 = 625 - 576 = 49 = 7^2\)

⇒ \(r = 7cm\)