2007 AIME II Problem 11

Two long cylindrical tubes of the same length but different diameters lie
parallel to each other on a flat surface. The larger tube has radius 72 and rolls along the
surface toward the smaller tube, which has radius 24 . It rolls over the smaller tube and continues rolling along
the flat surface until it comes to rest on the same point of its circumference as it started, having made one
complete revolution. If the smaller tube never moves, and the rolling occurs with no slipping, the larger tube ends
up a distance x from where it starts. The distance x can be expressed in the form a \pi+b \sqrt{c}, where a, b,
and c are integers and c is not divisible by the square of any prime. Find a+b+c.