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minimal distance between circumcenters

Source: 2013 Oral Moscow Geometry Olympiad grades 8-9 p6

August 15, 2019
geometryMinimalminimumdistanceCircumcentercircumcircle

Problem Statement

Let ABCABC be a triangle. On its sides ABAB and BCBC are fixed points C1C_1 and A1A_1, respectively. Find a point P P on the circumscribed circle of triangle ABCABC such that the distance between the centers of the circumscribed circles of the triangles APC1APC_1 and CPA1CPA_1 is minimal.
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