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]
