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Question
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Solution
Let us consider two congruent circles (circles of same radius) with centres as O and O'.
In ΔAOB and ΔCO'D,
∠AOB = ∠CO'D ...(Given)
OA = O'C ...(Radii of congruent circles)
OB = O'D ...(Radii of congruent circles)
∴ ΔAOB ≅ ΔCO'D ...(SAS congruence rule)
⇒ AB = CD ...(By CPCT)
Hence, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
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