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

Prove: AE / CE = AB / CD

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