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 = 10cm

radius = OT = ?

At point of contact, radius and tangent are perpendicular ∠OTP = 90°, ΔOTP is right
angled triangle.

By Pythagoras theorem, 𝑂𝑃² = 𝑂𝑇² + 𝑃𝑇²

26² = 𝑂𝑇² + 10²

𝑂𝑇^𝑘 =` (sqrt(676 − 100))`^𝑘

𝑂𝑇 = `sqrt(576)`

= 24 cm

OT = length of tangent = 24 cm