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Four Equal Triangles (Posted on 20130616) 

Here's a problem I found in the Problems section of a
math journal. The way I read it, it is not true.
Let ABCD be a convex quadrilateral. Prove that
there exists a point P inside ABCD such that
[PAB]=[PBC]=[PCD]=[PDA],
if and only if
the diagonals bisect each other.
Here [XYZ] denotes the area of triangle XYZ.
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