Question

P is in exterior of ⦿ (O, 15). A tangent from P touches the circle at T. If PT = 8, then OP = .....,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 17
(b) 13
(c) 23
(d) 7

Answer 1

We know, tangent of circle at point of contact making right angle with the radius.

Hence, using Pythagoras Theorem in ΔOTP

$OT^{2} +PT^{2} =OP^{2}$

$15^{2} +8^{2} =OP^{2}$

Hence, OP = 17

Option a is correct.

Answer 2

Option ( a ) is correct .

Explanation :

Given P is exterior of ( O , 15 ).

A tangent from P touches the circle

at T .

PT = 8 ,

OT = radius = 15 ,

We know that ,

OT perpendicular to PT .

[ radius , tangent relation ]

Now ,

In ∆OTP , <OTP = 90°

By Phythogarian theorem ,

OP² = OT² + PT²

= 15² + 8²

= 225 + 64

= 289

= 17²

OP = √17²

=> OP = 17

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