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Question

# O is the centre of the circle. AB is a chord of the circle. OM⊥AB. If AB=20 cm, OM=2√11 cm, then radius of the circle is

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

## The correct option is C 12 cmOA is the radius of the circlePerpendicular drawn from centre to a chord bisects the chord.Therefore AM=12ABAM=10cmThus, triangle OMA is right angled triangled at ∠OMA. ∠OMA=90∘.By Pythagoras theorem,OA2=OM2+MA2 OA=√OM2+MA2 OA=√(2√11)2+102OA=√144cmOA=12cmRadius of a circle is 12cm.Option B will be the answer.

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