A point P is at a distance 13 cm from the centre C of a circle, and PT is a tangent to the given circle. If PT = 12 cm, find the radius of the circle.

The below diagram shows the circle and the tangent: Given point P is 13 cm away from centre C, so CP = 13 cm. PT = 12 cm CT = radius of the circle. Since the tangent at any point of a circle and the radius through the point are perpendicular to each other. So, CT ⊥ PT So, in right angled △CPT by pythagoras theorem, Hence, radius of circle = 5 cm.