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.

(In reply to re: Solution by Bractals)

Yes that would do it.  It is conceivable that the author of the problem had that in mind originally and someone thought they were neatening it up by changing it.

Posted by Jer on 2013-06-17 15:13:56