# Problem #1119

 1119 Three pairwise-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? $\mathrm{(A) \ } 3+\dfrac{\sqrt{30}}{2} \qquad \mathrm{(B) \ } 3+\dfrac{\sqrt{69}}{3} \qquad \mathrm{(C) \ } 3+\dfrac{\sqrt{123}}{4} \qquad \mathrm{(D) \ } \dfrac{52}{9} \qquad \mathrm{(E) \ } 3+2\sqrt{2}$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
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