Napoleon's Triangle

Given a triangle ABC we can construct equilateral triangles on the outsides of the triangle. The circumcircles of these triangles meet in a point called the Fermat point and the centres of the circumcircles form a fourth equilateral triangle -- the Napoleon triangle.

It is also interesting to note that the centroid of the Napoleon triangle is the centroid of the original triangle.

To watch the Napolean triangle in a GSP sketch click here.

For a discussion on why the Napoleon triangle is equilateral click here.

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