Apollonius Pursuit Problem

Given a ship with a known constant direction and speed $v$, what course should be taken by a chase ship in pursuit (traveling at speed $V$) in order to intercept the other ship in as short a time as possible? The problem can be solved by finding all points which can be simultaneously reached by both ships, which is an Apollonius Circle with $\mu=v/V$. If the Circle cuts the path of the pursued ship, the intersection is the point towards which the pursuit ship should steer. If the Circle does not cut the path, then it cannot be caught.

See also Apollonius Circles, Apollonius' Problem, Pursuit Curve

References

Ogilvy, C. S. Solved by M. S. Klamkin. ``A Slow Ship Intercepting a Fast Ship.'' Problem E991. Amer. Math. Monthly 59, 408, 1952.

Ogilvy, C. S. Excursions in Geometry. New York: Dover, p. 17, 1990.

Steinhaus, H. Mathematical Snapshots, 3rd American ed. New York: Oxford University Press, pp. 126-138, 1983.