A problem by Yahia El Haw

Level pending

\(ABCD\) is a parallelogram. \(E\) is a point on it. \(\overrightarrow { ED } \) is a bisector for \(\hat { (ADC) } \). \(\overrightarrow { EC } \) is a bisector for \(\hat { (DCB) } \) .\(F\) is the midpoint of \(DC\).

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