# Triangle with an Altitude

Geometry Level 4

$$ABC$$ is a right triangle with $$\angle ABC = 90^\circ$$. Point $$D$$ is the midpoint of $$BC$$, and point $$E$$ is the foot of the perpendicular from $$B$$ to $$AC$$. $$AD$$ and $$BE$$ intersect at $$F$$. If $$AB = 36$$ and $$\angle BAD = \angle BCA$$, what is the value of $$FE^2$$?

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