<span lang="EN-US

Draw, OPAB and OQCD

In triangle OBP and triangle OQC,

∠OPB = ∠OQC [Angle = 90°]

∠OBP = ∠OCD [Alternate angle]

OB = OC [Radius]

By side-angle-side criterion of congruence

ΔOBP ≅ ΔOQC

∴ OP = OQ

The chords equidistant from the center are equal.

∴ AB = CD Proved.