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locus of points in square, triangle centers

Source: Serbia MO 2006 2nd Grade P2

April 10, 2021
geometry

Problem Statement

For an arbitrary point MM inside a given square ABCDABCD, let T1,T2,T3T_1,T_2,T_3 be the centroids of triangles ABM,BCMABM,BCM, and DAMDAM, respectively. Let OMOM be the circumcenter of triangle T1T2T3T_1T_2T_3. Find the locus of points OMOM when MM takes all positions within the interior of the square.
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