2004 AMC 10A Problem 25

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?

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

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