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
Solution by Bractals)
I followed you all the way up to this:
"Then the point of contact of
the third sphere, of radius a, will fall on the
intersection of the two circles."
I assume by "the two circles" you mean the projection of the spheres straight down onto the x-y plane, right?
But I still don't understand. The point of contact of the third sphere and...what? The other spheres? That's two points. The plane that the square (table top) is in? But that's not on the edge of the square.
Otherwise, this looks like a good analysis--I got the same result for the first 2 spheres, but that's obviously the easy part of this puzzle.
re: Solution
