In the figure below the triangle DEF results from ABC by applying 5 times the procedure.

The problem is related to the one of finding the triangle with maximal area inscribed in a given circle. The answer is the equilateral. Since, applying the previous procedure to one with two non equal sides gives a triangle with greater area. See the file MaximalTrianglesInEllipse.html for an application of this maximality property of equilaterals.

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