Question

If PT is a tangent at T to a circle whose center is O and OP = 17 cm, OT = 8 cm. Find the length of tangent segment PT.

Answer 1

OT = radius = 8cm

OP = 17cm

PT = length of tangent = ?

T is point of contact. We know that at point of contact tangent and radius are perpendicular.

∴ OTP is right angled triangle ∠OTP = 90°, from Pythagoras theorem 𝑂𝑇² + 𝑃𝑇² = 𝑂𝑃²

8² + 𝑃𝑇² = 17²

`PT sqrt(17^2 − 8^2) = sqrt(289 − 64)`

=`sqrt(225)` = 15𝑐𝑚

∴ PT = length of tangent = 15 cm.