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 Two circles (Posted on 2004-10-21)
In a 8½x11 sheet of paper I drew two equal non-overlapping circles -- both completely inside the paper, of course.

What's the largest portion of the paper I could cover with the circles?

What would be the answer if I drew THREE equal circles?

 No Solution Yet Submitted by Federico Kereki Rating: 3.2500 (4 votes)

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 re: Two circles case--further explanation | Comment 2 of 11 |
(In reply to Two circles case by David Shin)

Specifically, a line joining the centers of the two circles is the diagonal of a rectangle with opposite corners at those centers. These centers are r units away from the edges, leading to an equation, by the Pythagorean Theorem:

(2r)^2 = (8.5-2r)^2 + (11-2r)^2

which is equivalent to

4r^2 - 78r + 8.5^2 + 11^2 = 0,

the lower solution of which leads to David's answer (2.9126...), the larger solution being outside the rectangle.

 Posted by Charlie on 2004-10-21 17:20:06

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