Question

A tangent from P, a point in the exterior of a circle, touches the circle at Q. If OP = 13,PQ = 5, then the diameter of the circle is ......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 576
(b) 15
(c) 8
(d) 24

Answer 1

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

Hence, using Pythagoras Theorem in ΔOQP

$OQ^{2} +PQ^{2} =OP^{2}$

$OQ^{2} +5^{2} = 13^{2}$$OQ^{2} =13^{2} -5^{2}$

$OQ^{2} = 12^{2}$

Hence, OQ = 12

Here, OQ is radius so daimeter is 2OQ = 24

Option d is correct.

Answer 2

Option ( d ) is correct .

Explanation :

OQ = √( OP² - PQ² )

= √( 13² - 5² )

= √ ( 169 - 25 )

= √144

OQ = 12

Therefore ,

diameter ( d ) = 2 × radius

=> d = 2 × OQ

=> d = 2 × 12

=> d = 24

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