The larger sphere would never be able to rest on two smaller spheres without falling... This question = FAIL!
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?
The answer is 3+ root 69/3.
I really can't think of an approach, yet...
2. The center M of the larger sphere is vertically above the centroid F of the isosceles triangle. The larger sphere is tangent to all three smaller spheres.
3. is a right triangle with
4. You have to add one small radius and one large radius to the distance and you'll get the given result.
5. For additional information have a look here: Close-packing of spheres - Wikipedia, the free encyclopedia