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

Question

(A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm

Answer 1

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

∴ OP ⊥ PQ
also, ΔOPQ is right angled.
OQ = 25 cm and PQ = 24 cm (Given)

By Pythagoras theorem in ΔOPQ,

OQ² = OP² + PQ²
⇒ (25)² = OP² + (24)²

⇒OP² = 625 - 576

⇒OP² = 49

⇒OP = 7 cm

Option (A) is correct