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?
Question:
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?
Answer:
Let's think step by step.

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3+ \frac{\sqrt{69}}{3}
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?
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