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Question

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, Calculate the radius of the circle.


A

12.25 cm

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B

21.10 cm

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C

11.25 cm

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D

13.95 cm

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Solution

The correct option is C

11.25 cm


OBA=90

(Radius throught the point of contact is perpendicular to the tangent)

OB2=OA2AB2 [By Pythagoras Theorem]
r2=(r+7.5)2152

r2=r2+56.25+15r225

15r=168.75
r=168.7515r=11.25

Hence, radius of the circle =11.25 cm


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