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(2): Solution by Bractals)
Aha! Very good. That did help... a lot.
I misread your original post; I thought this phrase ended with a period: "Then the point of contact of the third sphere, of radius a, will fall on the intersection of the two circles," and that "two circles" was a reference to something above. Instead, the "two circles" are defined by the equations (1) and (2) below that phrase. Now I see that the two circles are defined in terms of the 3rd sphere, and would be located differently depending on that sphere's size (radius a). Where those circles intersect are the location(s) where the third sphere is tangent to both the original spheres, as well as the table. Now, all you do is adjust the value a, until one of the points of intersection of the two circles lies on the edge of the table.
Good job.
Edited on June 21, 2005, 3:19 am
re(3): Solution
