IMO 2015 Shortlist G5
Let ABC be a triangle with CA ‰ CB. Let D, F, and G be the midpoints of the sides AB, AC, and BC, respectively. A circle...
Category: Geometry
Problem
Let ABC be a triangle with CA ‰ CB. Let D, F, and G be the midpoints of the sides AB, AC, and BC, respectively. A circle Γ passing through C and tangent to AB at D meets the segments AF and BG at H and I, respectively. The points H1 and I1 are symmetric to H and I about F and G, respectively. The line H1 I1 meets CD and FG at Q and M, respectively. The line CM meets Γ again at P. Prove that CQ “ QP. (El Salvador)