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Prove that In equal circles (or in the same circle) if two arcs are equal, they subtend equal angles at the centres.

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In equal circles (or in the same circle) if two arcs are equal, they subtend equal angles at the centres.

Data:

In equal circles AXB and CYD, equal arcs AMB and CND subtend ∠APB and ∠CQD at the centres P and Q respectively.

To Prove:

∠APB=∠CQD

Proof:

In case of the same circle:

Fig.(ii) and fig.(iii) may be considered to be two equal circles obtained from fig.(i) and then the above proofs may be applied.

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