AMC 12 2004a 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?

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