Given 3 points on a plane, all 3 at the same semi-plane defined by a line (e), find a point P on the line (e) for which the sum of lengths of the 3 segments that are defined (by each of the 3 points and the point on the line), is minimal.
I think that we must draw the projections of each of the 3 initial points A, B, C, say, A', B' and C' and then take the middle point M of A'B', then the middle point N of MC' and point N is the one we ask - or something like this. But even if it is correct, I don't know how to prove it :( Any ideas are much appreciated!