Fermat point or Torricelli point

One of the fun topic I taught in last couple of days is the Fermat point and Torricelli point. This is a point inside a triangle such that its total distance from all three vertices is minimum. We sometimes also define this point as one which makes an angle of 120 degree with the sides of the triangle.

  To find this point
1. Construct equilateral triangle on the sides of the original triangle.
2. Draw circumcircle of these equilateral triangles.
3. The point where these two circles intersect (ofcourse other than the common vertex) will be the Fermat point.

In my drawing that point is Q and D is a random point and you should observer that when D coincide with Q we have the least sum. Also note the angles