Question

A point P is 25 cm away from the centre of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.

Answer 1

Let O be the center of circle, OP = 25 cm (given)

Let T be the any point on the circle, then PT = 24 cm

To Find: Radius of the circle

From Figure:

OT ⊥ PT

In right ∆OPT,

By Pythagoras Theorem:

OP² = OT² + PT²

25² = OT² + (24)²

625 = OT² + 576

OT = 7

Radius of the circle is 7 cm.