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Question

In two concentric circles with centre O, if AD is the chord of the larger circle, then AB = CD.


A

True

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B

False

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Solution

The correct option is A

True


Draw OM ⊥ AD.
OM bisects AD as OM ⊥ AD.
( perpendicular from the centre of a circle to its chord bisects the chord)
⇒ AM = MD --- (i)
OM bisects BC as OM ⊥ BC.
( perpendicular from the centre of a circle to its chord bisects the chord)
⇒ BM = MC --- (ii)
From (i) and (ii),
AM - BM = MD - MC
⇒ AB = CD


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