Given: Points C,E,B and A,E,D are collinear

Prove: AE / CE = AB / CD

∠DAB =∠DCB
∠DAB=(1/2) * (arc DB) and ∠DCB=(1/2) * (arc DB)
Inscribed angle measures half its intercepted arc
AA similarity
∠AEB = ∠CED
△AEB ~ △CED
Definition
Substitution
AE / CE = AB / CD
Vertical angles are equal