Sarthaks Test
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Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

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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] 

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