IMO Shortlist 2010 problem G4

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Dodao/la: arhiva
23. lipnja 2013.
Given a triangle ABC, with I as its incenter and \Gamma as its circumcircle, AI intersects \Gamma again at D. Let E be a point on the arc BDC, and F a point on the segment BC, such that \angle BAF=\angle CAE < \dfrac12\angle BAC. If G is the midpoint of IF, prove that the meeting point of the lines EI and DG lies on \Gamma.

Proposed by Tai Wai Ming and Wang Chongli, Hong Kong
Izvor: Međunarodna matematička olimpijada, shortlist 2010