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

Prove: AE / CE = AB / CD

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