Prove: Angle DAB Bisector when Given Parallelogram ABCD, Cyc. Quadrilateral BCED

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Consider five points A, B, C, D and E such that ABCD is a parallelogram and BCED is a
cyclic quadrilateral. Let l be a line passing through A. Suppose that l intersects the interior
of the segment DC at F and intersects line BC at G. Suppose also that EF = EG = EC.
Prove that l is the bisector of angle DAB.
 
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Can you give a drawing? ( I'm a bit lazy )
 

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