Given : Two congruent circles with centres O and O′. AB and CD are equal chords of the circles with centres O and O′ respectively.
To Prove : ∠AOB = ∠COD
Proof : In triangles AOB and COD,
AB = CD [Given]
AO = CO '
BO = DO ' [Radii of congruent circle]
⇒ ∆AOB ≅ ∆CO′D [SSS axiom]
⇒ ∠AOB ≅ ∠CO′D Proved. [CPCT]