Prove that equal chords of a circle subtend equal angles at the centre.
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Consider two congruent circles having centre O and O' and two chords AB and CD of equal lengths.
In ΔAOB and ΔCO'D,
AB = CD (Chords of same length)
OA = O'C (Radii of congruent circles)
OB = O'D (Radii of congruent circles)
∴ ΔAOB ≅ ΔCO'D (SSS congruence rule)
⇒ ∠AOB = ∠CO'D (By CPCT)
Hence, equal chords of congruent circles subtend equal angles at their centres.