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Reflection lies on circumcircle

Source: Swiss MO 2023/1

March 12, 2023
geometrygeometric transformationreflectioncircumcircle

Problem Statement

Let ABCABC be an acute triangle with incenter II. On its circumcircle, let MAM_A, MBM_B and MCM_C be the midpoints of minor arcs BC,CABC, CA and ABAB, respectively. Prove that the reflection MAM_A over the line IMBIM_B lies on the circumcircle of the triangle IMBMCIM_BM_C.
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