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Area phae = area pebf = area pfcg = area pgdh.

Source: Problem 4, Brazilian MO, 1990

March 19, 2006
geometryratiogeometry proposed

Problem Statement

ABCDABCD is a quadrilateral, E,F,G,HE,F,G,H are midpoints of AB,BC,CD,DAAB,BC,CD,DA. Find the point P such that area(PHAE)=area(PEBF)=area(PFCG)=area(PGDH)area (PHAE) = area (PEBF) = area (PFCG) = area (PGDH).
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