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.
Prove that if chords of congruent circles suhtend caual angles at their centres then​

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