# Area from a Perpendicular Sum

Geometry Level 3

$$ABCD$$ is a convex cyclic quadrilateral such that $$AB = AD$$ and $$\angle BAD = 90^\circ$$. $$E$$ is the foot of the perpendicular from $$A$$ to $$BC$$, and $$F$$ is the foot of the perpendicular from $$A$$ to $$DC$$. If $$AE + AF = 16$$, what is the area of $$ABCD$$?

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