CEMC Hypatia, 2004

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, triangle $OMN$ has vertices $O(0,0)$ , $M(6,0)$ and $N(0,8)$ . Determine the coordinates of point $P(a,b)$ inside the triangle so that the areas of the triangles $POM$ , $PON$ and $PMN$ are all equal.

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