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K Sengupta
Posts:
114
From:
INDIA
Registered:
1/10/06


A Quadrilateral Puzzle
Posted:
Apr 16, 2006 11:59 AM


In the convex quadrilateral ABCD, the diagonals AC and BD are perpendicular and the opposite sides AB and DC are not parallel. Suppose that the point P, where the perpendicular bisectors of AB and DC meet, is inside ABCD. Prove that ABCD is a cyclic quadrilateral if and only if the triangles ABP and CDP have equal areas.



