IMO 2011 Shortlist G5
Let ABC be a triangle with incenter I and circumcircle ω. Let D and E be the second intersection points of ω with the li...
Category: Geometry
Problem
Let ABC be a triangle with incenter I and circumcircle ω. Let D and E be the second intersection points of ω with the lines 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 ω at A and at B meet at a point K. Prove that the three lines AE, BD, and KP are either parallel or concurrent.