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...
1. The centers of the smaller spheres form a isosceles triangle with the side-length 2.
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
hypotenuse
horizontal leg
vertical leg
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