Question

AB and CD are two parallel chords of a circle whose diameter is AC. Prove that AB = CD.

Answer 1

$\Delta AOB\cong \Delta COD$ (ASA)

$\angle CAB=\angle ACD$ (alternate angles)

$\angle COD=\angle AOB$ (vertically opposite angles)

$AO=OC$ (radius)

So, AB = CD (By corresponding parts of congruent triangle)