General's Horse: Shortest Path Challenge

An interactive game to solve the classic General's Horse problem, finding the shortest path using geometric reflection.

A general, located at point B, needs to ride to the river to let his horse drink, and then proceed to his barracks at point A. To save time and conserve the horse's energy, the general wants to find the point on the riverbank that will make his total travel distance (from B to the river, then to A) the shortest possible. Your challenge is to find this optimal point.