Question

Prove that equal chords of a circle subtend equal angle at centre

Answer 1

Given : In a circle C(O,r), chord AB = chord CD.

To Prove : ∠AOB = ∠COD.

Proof : In△AOB and △COD

AO = CO [radii of same circle]

BO = DO [radii of same circle]

Chord AB = Chord CD [given]

⇒ △AOB ≅ △COD [by SSS congruence axiom]

⇒ ∠AOB = ∠COD. [c.p.c.t.]