MathDB
Taiwanese Geometry

Source: 2019 Taiwan TST Round 2

April 1, 2020
geometrycircumcircle

Problem Statement

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