Question : If PT is a tangent at T to a circle whose centre is O and OP = 17 cm and OT = 8 cm, find the length of the tangent segment PT.
Option 1: 13 cm
Option 2: 14 cm
Option 3: 16 cm
Option 4: 15 cm
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Correct Answer: 15 cm
Solution :
Let the tangent drawn from point P to the circle meet it at point T.
Let O be the centre of the circle
Given, OP = 17 cm and OT = 8 cm
We know that tangent makes a right angle with radius at the point of contact.
So, $\angle$ OTP = 90°
Using Pythagoras theorem in triangle OTP,
OP
2
= OT
2
+ PT
2
⇒ 17
2
= 8
2
+ PT
2
⇒ PT = 15 cm
Hence, the correct answer is 15 cm.
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