OP bisects AB and OQ bisects CD

Substitution

AP = CQ

Substitution

Equal arcs have equal chords

AB = AP + PB and CD = CQ + QD

AP + PB = CQ + QD

Definition

Algebra

If a diameter is perpendicular to a chord, it bisects the chord

AP + AP = CQ + CQ

OP ⟂ AB and OQ ⟂ CD

AP = PB and CQ = QD

AB = CD

Given

Segment addition theorem