Substitution

AP + PB = CQ + QD

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

Algebra

Equal arcs have equal chords

AP + AP = CQ + CQ

Substitution

AP = CQ

AB = AP + PB and CD = CQ + QD

OP bisects AB and OQ bisects CD

OP ⟂ AB and OQ ⟂ CD

Definition

AP = PB and CQ = QD

AB = CD

Given

Segment addition theorem