Hello, john128!

1. 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.

DrawCode:A B H o---------------o o | | * Y* | * |θ * | * Z+ - - - oE | * | *: | * | * : | G o | *θ : | * D o---*---+-------o C * *X W o F

Draw

Let

In

In

Since , then

Hence, is equidistant from sides and

That is, is on the bisector of

Therefore, is on the diagonal