Problem

Source: 2019 Taiwan TST Round 2

Tags: geometry, circumcircle



Given a triangle ABC. Denote its incircle and circumcircle by ω,Ω, respectively. Assume that ω tangents the sides AB,AC at F,E, respectively. Then, let the intersections of line EF and Ω to be P,Q. Let M to be the mid-point of BC. Take a point R on the circumcircle of MPQ, say Γ, such that MREF. Prove that the line AR, ω and Γ intersect at one point.