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 centre.

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Answer 1

Answer:

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Answer 2

Explanation:

Let us consider a circle with center O and two equal chords of a circle AB and CD.

We need to prove that ∠AOB=∠COD

In △ AOB and COD,  we have 

AO=CO  (Radius of the circle) 

BO=DO  (Radius of the circle) 

AB=CD  (Equal chords)

By SAS criterion of congruence, we have 

△AOB≅△COD

⇒∠AOB=∠COD