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IMO Shortlist 2012, Geometry 2

Source: IMO Shortlist 2012, Geometry 2

July 29, 2013
geometryparallelogramreflectioncircumcircleIMO Shortlistmoving pointsptolemy sinus lemma

Problem Statement

Let ABCDABCD be a cyclic quadrilateral whose diagonals ACAC and BDBD meet at EE. The extensions of the sides ADAD and BCBC beyond AA and BB meet at FF. Let GG be the point such that ECGDECGD is a parallelogram, and let HH be the image of EE under reflection in ADAD. Prove that D,H,F,GD,H,F,G are concyclic.
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