IMO 2020 Shortlist G7
Let P be a point on the circumcircle of an acute-angled triangle ABC. Let D, E, and F be the reflections of P in the mid...
Category: Geometry
Problem
Let P be a point on the circumcircle of an acute-angled triangle ABC. Let D, E, and F be the reflections of P in the midlines of triangle ABC parallel to BC, CA, and AB, respectively. Denote by ωA, ωB, and ωC the circumcircles of triangles ADP, BEP, and CFP, respectively. Denote by ω the circumcircle of the triangle formed by the perpendicular bisectors of segments AD, BE and CF. Show that ωA, ωB, ωC, and ω have a common point. (Denmark)