Two teams relay race: members of a team of three take turns running from the point P to a points on the circle; A for the first, B for the second, and C for the third, starting and returning at point P, transferring the baton at point P.
The points A, B, and C are set by the organizers of the competition.
Assuming that all runners have the same rate, each team selects the point P for the other team. Your task to maximize the length of the run for the competitors, by selecting the best point P to improve your probability to beat the competition.
The basic mathematical problem can be described as follows:
Given three points $A$, $B$, and $C$ and the circle that goes through them, find the point $P$ on the circle that maximizes $PA + PB + PC$.