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Question

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

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

## The correct option is B 13 cmLet OP=x cm ∴OQ=(17−x) cm∵AB=10cm⟹AP=5 cm ........... [∵OP is a straight line from centre]In ΔAOP,(OA)2=(AP)2+(OP)2r2=(5)2+x2r2=x2+25 ...... (i)∵CD=24 cm⟹CQ=12 cmAgain in ΔOCQ,(OC)2=(CQ)2+(OQ)2r2=(12)2+(17−x)2r2=144+289+x2−34x ....... (ii)From (i) and (ii), we getx2−34x+289+144=x2+25⟹34x=408⟹x=12 cmSubstituting the value of x in (i), we getr2=(12)2+25=144+25=169 cm2⟹r=13 cmHence, radius of circle is 13 cm

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