Question

Prove that if chords of congurent circle subtend equal angle at their centres then the chords are equal.

Answer 1

let the two circles with centre O and P are congruent circles, therefore their radius will be equal.

given: AB and CD are the chords of the circles with centres O and P respectively.

∠AOB=∠CPD

TPT: AB=CD

proof:

in the ΔAOB and ΔCPD

AO=CP=r and OB=PD=r

∠AOB=∠CPD

therefore by SAS congruency, ΔAOB and ΔCPD are congruent triangle.

therefore AB=CD

Answer 2

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