Question

A point P is 26 cm away from O of circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

Answer 1

Given, OP = 26 cm

PT = length of tangent = 10 cm

To find: radius = OT = ?

We know that,

At point of contact, radius and tangent are perpendicular ∠OTP = 90°

So, ∆OTP is right angled triangle.

Then by Pythagoras theorem, we have

OP² = OT² + PT²

26² = OT² + 10²

OT² = 676 – 100

OT = √576

OT = 24 cm

Thus, OT = length of tangent = 24 cm