CEMC Hypatia, 2004

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, quadrilateral $OMLK$ has vertices $O(0,0)$ , $M(6,0)$ , $L(10,t)$ , and $K(0,t)$ , where $t > 0$ . Show that there is no point $Q(c,d)$ inside the quadrilateral so that the areas of the triangles $QOM$ , $QML$ , $QLK$ , and $QKO$ are all equal.

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