Definition
AB = AP + PB and CD = CQ + QD
If a diameter is perpendicular to a chord, it bisects the chord
OP ⟂ AB and OQ ⟂ CD
Substitution
AP + AP = CQ + CQ
OP bisects AB and OQ bisects CD
Equal arcs have equal chords
AP + PB = CQ + QD
Substitution
Algebra
AP = CQ