IMO 1992 LL AUS1

Points D and E are chosen on the sides AB and AC of the

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IMO 1992 LL AUS1

Origin: AUS

Problem

Points D and E are chosen on the sides AB and AC of the triangle ABC in such a way that if F is the intersection point of BE and CD, then AE + EF = AD + DF. Prove that AC + CF = AB + BF.