IMO Shortlist 2011 problem G5

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Dodao/la: arhiva
June 23, 2013
Let ABC be a triangle with incentre I and circumcircle \omega. Let D and E be the second intersection points of \omega with AI and BI, respectively. The chord DE meets AC at a point F, and BC at a point G. Let P be the intersection point of the line through F parallel to AD and the line through G parallel to BE. Suppose that the tangents to \omega at A and B meet at a point K. Prove that the three lines AE,BD and KP are either parallel or concurrent.

Proposed by Irena Majcen and Kris Stopar, Slovenia
Source: Međunarodna matematička olimpijada, shortlist 2011