The One-Cushion Escape from Snooker in a Circular Table

The one-cushion escape from snooker in a circular table can be viewed as a ge-ometric problem involving the reflection of a light ray in a circular mirror. There are at most four escapes in any given configuration. We will obtain specific configurations in which there are exactly 0, 1, 2, 3 or 4 escapes. The details consist in determining the number of real solutions in the interval (−1; 1) of certain polynomial equations, of degrees two, three or four.