Ex 10.2, 2

Transcript

Ex 10.2, 2 Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal. Given: Two congruent circles C1 & C2 AB is the chord of C1 & PQ is the chord of C2 & ∠ AOB = ∠ PXQ To prove: Chords are equal, i.e., AB = PQ Proof: In ∆ AOB & ∆ PXQ AO = PX ∠ AOB = ∠ PXQ BO = QX ∆ AOB ≅ ∆ PXQ ∴ AB = PQ