IMO 2020 Shortlist G8
Let Γ and I be the circumcircle and the incenter of an acute-angled triangle ABC. Two circles ωB and ωC passing through ...
Category: Geometry
Problem
Let Γ and I be the circumcircle and the incenter of an acute-angled triangle ABC. Two circles ωB and ωC passing through B and C, respectively, are tangent at I. Let ωB meet the shorter arc AB of Γ and segment AB again at P and M, respectively. Similarly, let ωC meet the shorter arc AC of Γ and segment AC again at Q and N, respectively. The rays PM and QN meet at X, and the tangents to ωB and ωC at B and C, respectively, meet at Y . Prove that the points A, X, and Y are collinear. (Netherlands)