Prove that equal chords of a circle subtend equal angles at the centre.

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.