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

Prove: AE / CE = AB / CD

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