The sum of the distances is min (stage a)
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 B and C is min.
In each situation, the values of AP, BP+PC, and the values of the angles APB and APC are shown. The point P is dragged, and the smallest values of BP+PC is obtained when the two angles APB and APC are equal.