A square table (a meter a side) has two spheres on its surface. The spheres have two special properties:

1. The larger is twice the diameter of the smaller, and
2. They are the largest size that will fit on the table without falling off. (They may extend over the edge of the table.)

I. What are the dimensions of the spheres?

II. A third sphere is added next to the other two. What is its largest possible size?

(In reply to re: Solution by Ken Haley)

The two circles are (1) the circle centered
at the point of tangency of the smaller
sphere and the table with a radius of 2*a
(see preliminary remark) and (2) the circle
centered at the point of tangency of the 
larger sphere and the table with a radius
of 4*a (see preliminary remark). Their
"intersection" just happens to be circle (3)
which is the locus of points of contact 
between the third sphere and the table top
(if it was extended). Hope this helps.

Posted by Bractals on 2005-06-19 06:59:02