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 \( a + b \)?

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