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