MathDB
Problem: 2004 AMC 10 #25

Source:

February 1, 2007
geometry3D geometryspheretetrahedronratio

Problem Statement

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?
<spanclass=′latex−bold′>(A)</span>  3+302<spanclass=′latex−bold′>(B)</span>  3+693<spanclass=′latex−bold′>(C)</span>  3+1234<spanclass=′latex−bold′>(D)</span>  529<spanclass=′latex−bold′>(E)</span>  3+22 <span class='latex-bold'>(A)</span>\; 3+\frac{\sqrt{30}}2\qquad <span class='latex-bold'>(B)</span>\; 3+\frac{\sqrt{69}}3\qquad <span class='latex-bold'>(C)</span>\; 3+\frac{\sqrt{123}}4\qquad <span class='latex-bold'>(D)</span>\; \frac{52}9\qquad <span class='latex-bold'>(E)</span>\; 3+2\sqrt{2}
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