MathDB
equilateral triangle

Source: Ireland 1994

June 29, 2009
geometrycircumcircletrapezoidgeometric transformationrotationperpendicular bisectorgeometry proposed

Problem Statement

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