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Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
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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.
Concept: Angle Subtended by a Chord at a Point
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