2004 AMC 12A Problem 22

Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?

\text {(A) } 3 + \frac {\sqrt {30}}{2} \qquad \text {(B) } 3 + \frac {\sqrt {69}}{3} \qquad \text {(C) } 3 + \frac {\sqrt {123}}{4}\qquad \text {(D) } \frac {52}{9}\qquad \text {(E) }3 + 2\sqrt2

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.