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.

Options

• 5 cm

• 7 cm

• 10 cm

• 12 cm

Answer 1

5 cm

Explanation:

  

Since,

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

So, ∠OTP = 90°

So, in triangle OTP

(OP)² = (OT)² + (PT)²

13² = (OT)² + 12²

(OT)² = 13² − 12²

OT² = 25

OT = ${\displaystyle \sqrt{25}}$

OT = 5

So, radius of the circle is 5 cm.