Question

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

Answer 1

Given: $AB$ and $CD$ are two equal chords of a circle with a centre $O$.
To Prove: $\angle AOB=\angle COD$
Proof: In $\Delta AOB$ and $\Delta COD$,
$OA=OC$ (Radii of a circle)
$OB=OD$ (Radii of a circle)
and $AB=CD$ (Given)
$\therefore \Delta AOB\cong \Delta COD$ (By SSS-criterion of congruence)
By using corresponding parts of congruent triangles, we have
$\angle AOB=\angle COD$