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.

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#### Solution

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 𝑂𝑇^{2} + 𝑃𝑇^{2} = 𝑂𝑃^{2}

8^{2} + 𝑃𝑇^{2} = 17^{2}

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

=`sqrt(225)` = 15𝑐𝑚

∴ PT = length of tangent = 15 cm.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

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