#### Question

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

#### Solution

Since tangent to a circle is perpendicular to the radius through the point of contact.

∴ ∠OTP = 90°

In right triangle OTP, we have

`OP^2 = OT^2 + P^2`

`⇒ 13^2 = OT^2 + 12^2`

`⇒ OT^2 = 13^2 – 12^2`

= (13 – 12) (13 + 12) = 25

⇒ OT = 5

Is there an error in this question or solution?

Solution A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle. Concept: Circles Examples and Solutions.