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Question

# O is the centre of the circle having radius 5 cm. OM is a ⊥ on chord AB. If OM=4 cm, then the length of the chord AB is equal to

A
5 cm
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B
6 cm
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C
8 cm
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D
10 cm
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Solution

## The correct option is B 6 cmRadius of a circle is 5 cm.Therefore OB = 5 cm.Perpendicular drawn to the chord from the centre bisects the chord.Therefore AM = MBTriangle OMB is right angled triangle at M∠OMB=90∘By Pythagoras theorem;OB2=OM2+MB2MB=√OB2−OM2 MB=√52−42MB=3cmSo, the length of chord AB=2.(MB)=6cm.Option B will be the answer.

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