IMO Shortlist 1996 problem G4


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2. travnja 2012.
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Let ABC be an equilateral triangle and let P be a point in its interior. Let the lines AP, BP, CP meet the sides BC, CA, AB at the points A_1, B_1, C_1, respectively. Prove that

A_1B_1 \cdot B_1C_1 \cdot C_1A_1 \ge A_1B \cdot B_1C \cdot C_1A.
Izvor: Međunarodna matematička olimpijada, shortlist 1996