**Given : **Two congruent circles with centres O and O′. AB and CD are chords of circles with centre O and O′ respectively such that ∠AOB = ∠CO′D

**To Prove :** AB = CD

**Proof :** In triangles AOB and CO′D,

AO = CO′

BO = DO ⎬[Radii of congruent circle]

∠AOB = ∠CO′D [Given]

⇒ ∆AOB ≅ ∆CO′D [SAS axiom]

⇒ AB = CD **Proved.** [CPCT]