The vertex E of a square EFGH is inside a square ABCD. The vertices F, G and H are outside the square ABCD. The side EF meets the side CD at X and the side EH meets the side AD at Y. If EX = EY, prove that E lies on BD.
The quadrilateral EXDY is made up of two right triangles EXY and DYX. You also know that triangle EXY is isosceles.
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