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 $$a + b + c$$.

(第十六届AIME1998 第10题)