Question

1. 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

Step-by-step 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  

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