Consider a circle with center O, PQ is a tangent from point Q such that PQ = 24 cm and OQ = 25 cm i.e. distance of Q from center.

Consider a circle with center O, PQ is a tangent from point Q such that PQ = 24 cm and OQ = 25 cm i.e. distance of Q from center.

To find: Radius = OP

Now, ΔOPQ is a right-angled triangle at P as OP ⊥ PQ

[Tangent through a point on the circle is perpendicular to the radius through point of contact]

By Pythagoras theorem, we have

OP² + PQ² = OQ²

⇒ OP² + 24² = 25²

⇒ OP² + 576 = 625

⇒ OP² = 625 – 576 = 49

⇒ OP = 7 cm