Question

prove that equal chord of a circle subtend equal angle at the center

Answer 1

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Answer 2

Statement : Equal chords of a circle subtend equal angles at the centre.

Given : AB and CD are chords of a circle with centre O, such that AB = CD.

To prove : ∠AOC = ∠COD

Proof :

In ΔAOB and ΔCOD,

AO = CO [radii of same circle]
BO = DO [radii of same circle]
AB = CD [given]

ΔAOB ≅ ΔCOD [SSS]
∠AOB = ∠COD [C. P. C. T]

Hence, Equal chords of a circle subtend equal angles at the centre.