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Re: Overlapping circles
Posted:
Jun 9, 2001 7:48 AM


D & A Klinkenberg wrote: > > Hello W.H., > > The equation I get is: s = sqrt(d^2c^2)/2 + sqrt(4*d^2c^2)/2 + > 3*d/2. I don't think it is easy to solve for d, so I didn't try. The > square roots are intended to be the distance from the center of the > chord to the center of each circle. My guess is that an equation in > d^8 will result and I don't know whether that can be reduced.
If you're only interested in real solutions,
d = (9c^2  44k^2)/(72k)  (81 c^4 + 72 c^2 k^2  208 k^4)/(72k (729 c^6  972 c^4 k^2 + 3024 c^2 k^4 + 2240 k^6 + 144 Sqrt[3] k^3 Sqrt[ 81 c^6  144 c^4 k^2 + 368 c^2 k^4  64 k^6])^(1/ 3)) + (1/(72k)) ((729 c^6  972 c^4 k^2 + 3024 c^2 k^4 + 2240 k^6 + 144 Sqrt[3] k^3 Sqrt[ 81 c^6  144 c^4 k^2 + 368 c^2 k^4  64 k^6])^(1/3))
Thanks be to Mathematica (and careful retyping / reformatting and checking and rechecking).



