A geometry problem by Bryan MW

Geometry Level pending

In the figure above, trapezoid $$ABCD$$ has parallel lines $$AB$$ and $$CD$$ in the ratio $$6$$ :$$14$$ (their lengths). Given $$\angle$$$$AEC$$ = $$90^{\circ}$$, $$DE$$ = $$DB$$, calculate $$AE$$$$^{2}$$ .

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