IMO 2011 Shortlist G6
Let ABC be a triangle with AB = AC, and let D be the midpoint of AC. The angle bisector of ∠BAC intersects the circle th...
Category: Geometry
Problem
Let ABC be a triangle with AB = AC, and let D be the midpoint of AC. The angle bisector of ∠BAC intersects the circle through D, B, and C in a point E inside the triangle ABC. The line BD intersects the circle through A, E, and B in two points B and F. The lines AF and BE meet at a point I, and the lines CI and BD meet at a point K. Show that I is the incenter of triangle KAB.