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find the locus of centroid of a triangle

Source: Czech and Slovak third round,2006,p4

March 3, 2012
geometryincentergeometry proposed

Problem Statement

Given a segment ABAB in the plane. Let CC be another point in the same plane,H,I,GH,I,G denote the orthocenter,incenter and centroid of triangle ABCABC. Find the locus of MM for which A,B,H,IA,B,H,I are concyclic.
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