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$MI=MH$, where M is the midpoint of arc $AC$

Source: St. Petersburg MO 2001, 11th grade, P5

April 24, 2023
geometryorthocenterincentercircumcircle

Problem Statement

Let II and HH be the incenter and orthocenter of an acute triangle ABCABC. MM is the midpoint of arc ACAC of circumcircle of triangle ABCABC which does not contain point BB. If MI=MHMI=MH, find the measure of angle ∠ABC\angle ABC.
[I]Proposed by F. Bakharev
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