CEMC Galois, 2003

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, $ABCD$ is a square and the coordinates of $A$ and $D$ are as shown. The point $E(a, 0)$ is on the $x$ -axis so that the triangles $CBE$ and $ABE$ lie entirely outside the square $ABCD$ . For what value of $a$ is the sum of the areas of triangles $CBE$ and $ABE$ equal to the area of square $ABCD$ ?

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