IMO Shortlist 2012 problem G2

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3. studenoga 2013.
Let ABCD be a cyclic quadrilateral whose diagonals AC and BD meet at E. The extensions of the sides AD and BC beyond A and B meet at F. Let G be the point such that ECGD is a parallelogram, and let H be the image of E under reflection in AD. Prove that D,H,F,G are concyclic.
Izvor: Međunarodna matematička olimpijada, shortlist 2012