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IMO ShortList 1998, geometry problem 2

Source: IMO ShortList 1998, geometry problem 2

October 22, 2004
geometrycircumcircletrapezoidratioareaIMO Shortlist

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. Let EE and FF be variable points on the sides ABAB and CDCD, respectively, such that AE:EB=CF:FDAE:EB=CF:FD. Let PP be the point on the segment EFEF such that PE:PF=AB:CDPE:PF=AB:CD. Prove that the ratio between the areas of triangles APDAPD and BPCBPC does not depend on the choice of EE and FF.
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