IrMO 1994 P1 Q2: A Centroid of Centroids: Upper Secondary Mathematics Competition Question

Let A, B, C be three collinear points, with B between A and C. Equilateral triangles ABD, BCE, CAF are constructed with D and E on one side of the line AC and F on the opposite side. Prove that the centroids of the triangles are the vertices of an equilateral triangle. Prove that the centroid of this triangle lies on the line AC.


[IrMO 1994 P1 Q2]




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