Substitution

Definition

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

Algebra

AP = CQ

Substitution

Equal arcs have equal chords

OP bisects AB and OQ bisects CD

AB = AP + PB and CD = CQ + QD

AP + PB = CQ + QD

OP ⟂ AB and OQ ⟂ CD

AP + AP = CQ + CQ

AP = PB and CQ = QD

AB = CD

Given

Segment addition theorem