### Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

### Retracircles

Four circles all touch each other and a circumscribing circle. Find the ratios of the radii and prove that joining 3 centres gives a 3-4-5 triangle.

### A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

# Snookered

##### Stage: 4 and 5 Challenge Level:

Why do this problem?
The problem develops visualisation. Students may be interested because snooker is a popular game and they may be impressed that expert players can judge the angle of the shot accurately to bounce of two, three or even 4 walls and hit the target. One way to solve the problem is to use coordinates, similar triangles and gradients.

Possible approach
Work through one of the cases as a class together and then suggest that students draw a diagram. Then discuss the diagram as a class before the students calculate the various paths.

Key question
How can we turn into a straight line the path and the reflected path after the ball bounces off a cushion?

Possible support
Initially ignore the pink and blueballs which might be in the way of the shot.