Question

Prove that if chords or congruent circles subtend equal angles at their centres, then the chords are equal.

Answer 1

Circle with centres A and B are congruent and ∠PAQ = ∠RBS 

To Prove: PQ = RS. 

Proof: In ∆APQ and ∆BRS, 

AP = BR ……… radii of congruent circles 

AQ = BS are equal 

∠PAQ = ∠RBS (Data)

∴ ∆PQR ≅ ∆BRS (SAS postulate) 

∴ PQ = RS.