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Topic: Overlapping circles
Replies: 9   Last Post: Jun 17, 2009 2:06 AM

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 Lloyd Hugh Allen Posts: 11 Registered: 12/6/04
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^2-c^2)/2 + sqrt(4*d^2-c^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).