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 Perplexus Icon plus one (Posted on 2005-06-18)
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?

 See The Solution Submitted by Leming Rating: 4.5000 (6 votes)

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 re(2): Solution | Comment 4 of 12 |
(In reply to re: Solution by Ken Haley)

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`The two circles are (1) the circle centeredat the point of tangency of the smallersphere and the table with a radius of 2*a(see preliminary remark) and (2) the circlecentered at the point of tangency of the larger sphere and the table with a radiusof 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.`
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 Posted by Bractals on 2005-06-19 06:59:02

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