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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


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

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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