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Question

# AB and CD are two parallel chords of a circle such that AB=10 cm and CD=24 cm, if the chords are on the opposite sides of the centre and the distance between them is 17 cm, then the radius of the circle is

A
8 cm
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B
13 cm
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C
11 cm
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D
12 cm
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Solution

## The correct option is B 13 cmLet OP be x cm and radius be r cm.∴OQ=(17−x)cm∴In △OQC,(OC)2=(OQ)2+(QC)2r2=(17−x)2+(12)2.....(1)and in △OAP,(OA)2=(OP)2+(AP)2r2=x2+52....(2)On equating equation (1) and (2),∴(17−x)2+(12)2=x2+52⇒289−34x+x2+144=x2+25⇒34x=408∴x=12 cmr2=x2+52=(12)2+(5)2=144+25=169⇒r=13 cm.

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