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Geometry Mathley 9.4 fixed line

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June 7, 2020
geometryperpendicular bisectorincenterfixedfixed line

Problem Statement

Let ABCABC be a triangle inscribed in a circle (O)(O), and MM be some point on the perpendicular bisector of BCBC. Let I1,I2I_1, I_2 be the incenters of triangles MAB,MACMAB,MAC. Prove that the incenters of triangles AII1I2A_II_1I_2 are on a fixed line when MM varies on the perpendicular bisector.
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