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Find the locus of the centroid of the triangle [ILL 1974]

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January 2, 2011
geometry proposedgeometry

Problem Statement

Let C1C_1 and C2C_2 be circles in the same plane, P1P_1 and P2P_2 arbitrary points on C1C_1 and C2C_2 respectively, and QQ the midpoint of segment P1P2.P_1P_2. Find the locus of points QQ as P1P_1 and P2P_2 go through all possible positions. Alternative version. Let C1,C2,C3C_1, C_2, C_3 be three circles in the same plane. Find the locus of the centroid of triangle P1P2P3P_1P_2P_3 as P1,P2,P_1, P_2, and P3P_3 go through all possible positions on C1,C2C_1, C_2, and C3C_3 respectively.
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