The Fermat-Torricelli Problem Once More

This extremum problem is really a classical beauty. It has had a long and interesting history since it was formulated by Fermat in the 17th century. Given three points A , B and C , the task is to find a point P such that the sum of distances PA + PB + PC is minimal; (see Figure 1). After a few years Torricelli found the solution: P should be situated so that the angles between the half-lines PA , PB and PC are all 120° (except when one angle of the triangle ABC is greater than or equal to 120°). The solution has then been rediscovered many times in new and interesting ways.