Question

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Answer 1

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]