Question

prove that if chords of congruent circles subtend equal angles at their centers then the chords are equal​

Answer 1

Step-by-step explanation:

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