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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(2): Two circles case--further explanation | Comment 7 of 11 |
(In reply to re: Two circles case--further explanation by Charlie)

I think I agree with putting the circles in opposite corners and then expanding them until they are tangent to each other AND tangent to the sides of the paper.  Their centers being on 45 degree angles from the corners, but their tangent point will not be on this same line, but I guess we don't care. Working from center to center, we know:

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

Here's were I don't follow. When I expand this, I get:

4r^2 = (8.5)^2 - 17r + 4r^2 + (11)^2 - 22r + 4r^2
4r^2 = 8r^2 - 39r + (8.5)^2 + (11)^2
0 = 4r^2 - 39r + (8.5)^2 + (11)^2,  My question is where did your -78r term come from?

I would much rather have the 78, because when I plug my numbers into the quadratic formula, I end up having to take the square root of a neg number.

 Posted by bob909 on 2004-10-22 09:09:41

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