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Yet Another OI Geometry Problem

Source: 2022 Taiwan TST Round 2 Independent Study 1-G

April 7, 2022
geometryincentercircumcircleTaiwan

Problem Statement

Let II, OO, HH, and Ω\Omega be the incenter, circumcenter, orthocenter, and the circumcircle of the triangle ABCABC, respectively. Assume that line AIAI intersects with Ω\Omega again at point M≠AM\neq A, line IHIH and BCBC meets at point DD, and line MDMD intersects with Ω\Omega again at point E≠ME\neq M. Prove that line OIOI is tangent to the circumcircle of triangle IHEIHE.
Proposed by Li4 and Leo Chang.
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