IMO Shortlist 1998 problem G2


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2. travnja 2012.
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Let ABCD be a cyclic quadrilateral. Let E and F be variable points on the sides AB and CD, respectively, such that AE:EB=CF:FD. Let P be the point on the segment EF such that PE:PF=AB:CD. Prove that the ratio between the areas of triangles APD and BPC does not depend on the choice of E and F.
Izvor: Međunarodna matematička olimpijada, shortlist 1998