IMO 2018 Shortlist G5
Let ABC be a triangle with ir um ir le ω and in entre I. A line ℓ interse ts the lines AI, BI, and CI at points D, E, an...
Category: Geometry
Problem
Let ABC be a triangle with ir um ir le ω and in entre I. A line ℓ interse ts the lines AI, BI, and CI at points D, E, and F, respe tively, distin t from the points A, B, C, and I. The perpendi ular bise tors x, y, and z of the segments AD, BE, and CF, respe tively determine a triangle Θ. Show that the ir um ir le of the triangle Θ is tangent to ω. (Denmark)