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

Prove: AE / CE = AB / CD

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