Question

prove that equal chords of a circle subtend equal angles at the centre​

Answer 1

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 = ∠CODProof :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