A geometry problem by Lee Dongheng

Geometry Level 3

The figure shows a square \(ABCD\). \(E\) and \(F\) are selected on \(BC\) and \(CD\) respectively such that \(\angle DAF=\angle EAF\), \(AE=202\), \(BE=116\), find the length of \(DF\).

Note: The figure is not drawn to scale.

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