Question

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❥ 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.



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Answer 1

Answer:

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

Answer 2

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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