Question

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

Answer 1

Given: A circle with center $O$.

$AB$ and $CD$ are equal chords of the circle.

Proof:In $△AOB$ and $△DOC$

$AO=OD$ (radius)

$AB=CD$ (given)

$OB=OC$(radius)

$\therefore △AOB\cong △DOC$ by SSS rule

$\therefore \angle AOB=\angle DOC$ by CPCT

Hence proved.