# Stacked Spheres

Geometry Level 4

Three spheres of radius 10 are placed on a table all touching each other. A fourth sphere of radius 10 is placed so that it lies on top of the other three. The distance from the bottom of the fourth sphere to the table is $$h$$, and $$h^2 = \frac {a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

×