IR-MO 2003 Problem 2
assume ABCD a convex quadrilatral. P and Q are on BC and DC respectively such that angle BAP= angle DAQ .prove that [ADQ]=[ABP] ([ABC] means its area ) iff the line which crosses through the orthocenters of these traingles , is perpendicular to AC.
Dataset text AI-MO AoPS. Quoted with source.
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