In a 8½x11 sheet of paper I drew two equal nonoverlapping 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?
(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 = (8.52r)^2 + (112r)^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 20041021 17:20:06 