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 the circle is

(A) 7 cm (B) 12 cm

(C) 15 cm (D) 24.5 cm

Answer 1

Let O be the centre of the circle.

Given that,

OQ = 25cm and PQ = 24 cm

As the radius is perpendicular to the tangent at the point of contact,

Therefore, OP ⊥ PQ

Applying Pythagoras theorem in ΔOPQ, we obtain

OP² + PQ² = OQ²

OP² + 24² = 25²

OP² = 625 − 576

OP² = 49

OP = 7

Therefore, the radius of the circle is 7 cm.

Hence, alternative (A) is correct.