The sum of the distances is min (stage b)
The applet allows to investigate the task : Finding the location of the point P inside the triangle or outside the triangle, for which the sum of the distances from that point to the vertices of the triangle is min.
In this applet, one can drag the vertices A and C, and the point P, freely. The sum AP+BP+CP, and the values of the angles APB, APC and BPC are shown. The point P is dragged, and it is obtained that the smallest value of AP+BP+CP is when all three angles equal 120° (or when point P coincides with the vertex of the obtuse angle that is larger than or equal to 120°).