IMO 2015 Shortlist G2
Let ABC be a triangle inscribed into a circle Ω with center O. A circle Γ with center A meets the side BC at points D an...
Category: Geometry
Problem
Let ABC be a triangle inscribed into a circle Ω with center O. A circle Γ with center A meets the side BC at points D and E such that D lies between B and E. Moreover, let F and G be the common points of Γ and Ω. We assume that F lies on the arc AB of Ω not containing C, and G lies on the arc AC of Ω not containing B. The circumcircles of the triangles BDF and CEG meet the sides AB and AC again at K and L, respectively. Suppose that the lines FK and GL are distinct and intersect at X. Prove that the points A, X, and O are collinear. (Greece)