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

Philoid · Accepted Answer

Given:

OQ = 25 cm

PQ = 24 cm

Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆POQ is right-angled at ∠OPQ.

Therefore,

By Pythagoras Theorem in ∆POQ,

OP² + PQ² =OQ²

⇒ OP² = OQ² – PQ ²

⇒ OP= √( OQ² – PQ ²)

⇒ OP= √(25² – 24²)

⇒ OP= √(625 – 576)

⇒ OP = √49 cm

⇒ OP = 7 cm

Hence, OP = 7 cm