Yaglom's road
Northville and Southville lie on opposite sides of the Sticks River.
The townsfolk want to build a road and a bridge to facilitate travel
between their towns while minimizing the distance along the road.
[You can place the towns where you like by dragging the GREEN dots.
You can move the bridge by dragging the BLUE dot.]
Where should the bridge be located? What is true about the solution?
Can you prove your assertion?