Three logs each having diameter 4 feet are lying next to each other.  On top of these, and between them are lying two logs of diameter 2 feet.   What is the diameter of the log that could be placed on top of the stack just touching the two small logs and the middle log on the bottom?  (See the diagram on the left.)

For the more daring: What happens if the bottom logs have diameter a and the smaller logs above have diameter b?