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.