IMO Shortlist 2007 problem G4

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Dodao/la: arhiva
2. travnja 2012.
Consider five points A, B, C, D and E such that ABCD is a parallelogram and BCED is a cyclic quadrilateral. Let \ell be a line passing through A. Suppose that \ell intersects the interior of the segment DC at F and intersects line BC at G. Suppose also that EF = EG = EC. Prove that \ell is the bisector of angle DAB.

Author: Charles Leytem, Luxembourg
Izvor: Međunarodna matematička olimpijada, shortlist 2007