### Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

### Quartics

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

### Snooker

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

# Board and Spool

##### Age 16 to 18 Challenge Level:

A man is holding one end of a board and the another end is on a spool with the outer radius $R$ and the inner radius $r$. A board does not slip on the spool and the spool does not slip on the ground. The man starts to move with the board with a speed $u$.

1) How long does it take for the man to reach the spool?

2) Find the distance which must be traveled by the man to reach the spool.

3) Find the distance traveled by the man if $r = R$.

4) Calculate the time and the distance if $l = 298\mathrm{cm}$, $R = 101\mathrm{cm}$, $r = 86\mathrm{cm}$, $u = 1\mathrm{m/s}$.