Fermat Point

The Fermat point minimizes the sum of the distances from to the vertices of an acute triangle. In an acute triangle, the angle formed by the segments connecting any two vertices with is 120 degrees. Also, if one forms an equilateral triangle using two of the vertices of the original triangle, the third vertex of the equilateral triangle lies on a line through and the third vertex of the original triangle. These equilateral triangles are shown in gray.