The monster wants to catch the elusive tofubeast .

and are two points on a plane. is moving in direction (an angle clockwise relative to north) at a constant velocity . is the direction from to (angle of sight, relative to the same north), is the distance between them, and is the constant velocity of point . All these are given, and shown in Figure 1. Angles and are derived (from givens, and from the unknown direction in which will travel):

Suppose a point such that if and continue at their constant speeds and directions they will intercept at time . In other words, at any point in time , with seconds until interception, the points can be represented as shown in Figure 2, where is the rate at which points and are approaching. (Notice in particular the way assumptions of the problem are captured: an extant , and and constant over time.)

The problem:

- Make an expression for in terms of , ,
and .
- How many points are there for a given , , and
?