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**mathwizard** Consider five points $\displaystyle A, B, C, D$ and $\displaystyle E$ such that $\displaystyle ABCD$ is a parallelogram and

$\displaystyle BCED$ is a cyclic quadrilateral. Let $\displaystyle l$ be a line passing through $\displaystyle A$. Suppose

that $\displaystyle l$ intersects the interior of the segment $\displaystyle DC$ at $\displaystyle F$ and intersects line $\displaystyle BC$ at $\displaystyle G$. Suppose also that $\displaystyle EF = EG = EC$.

Prove that $\displaystyle l$ is the bisector of angle $\displaystyle DAB$.