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locus of medicenter, equilateral triangle

Source: Sharygin Finals 2022 8.3

October 3, 2022
geometry

Problem Statement

A circle ω\omega and a point PP not lying on it are given. Let ABCABC be an arbitrary equilateral triangle inscribed into ω\omega and A′,B′,C′A', B', C' be the projections of PP to BC,CA,ABBC, CA, AB. Find the locus of centroids of triangles A′B′C′A' B'C'.
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