CEMC Galois, 2003

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

The point $F$ is on the line passing through the points $M(6, -1)$ and $N(12, 2)$ so that the triangles $CBF$ and $ABF$ lie entirely outside the square $ABCD$ . Determine the coordinates of the point $F$ if the sum of the areas of triangle $CBF$ and $ABF$ equals the area of square $ABCD$ .

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