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.
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.