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.
