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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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ℚ
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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:
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
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
i hope its helpful for you