1998 AIME Problem 10

Eight spheres of radius 100 are placed on a flat surface so that each sphere is tangent to two others and their centers are the vertices of a regular octagon. A ninth sphere is placed on the flat surface so that it is tangent to each of the other eight spheres. The radius of this last sphere is a+b \sqrt{c}, where a, b, and c are positive integers, and c is not divisible by the square of any prime. Find a+b+c.