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What I am want to know is the size of the circle that would maximally fill in the space between the three larger circles. Any ideas? I'm thinking calculus min or maximization problem.

Any references, ideas or pointers appreciated.

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- Thread starter klawlor419
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- #1

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What I am want to know is the size of the circle that would maximally fill in the space between the three larger circles. Any ideas? I'm thinking calculus min or maximization problem.

Any references, ideas or pointers appreciated.

- #2

Simon Bridge

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If you have already solved for the radius of the three circles - then these will define three points on the inner circle and thus the circle itself can be found.

i.e. the inner circle you are finding is centered at (0,0), and the upper circle is centered at (0,y), and has radius r, then the radius of the inner circle is y-r

- #3

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ratio(outer:inner)=(2/3)Sqrt[3]-1

Can this be confirmed? Thanks again

- #4

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You might want to look at http://en.wikipedia.org/wiki/Descartes'_theorem]Descartes'[/PLAIN] [Broken] Theorem. Or you could draw a bunch of line segments (such as those connecting the centres of the circles and the radii tangent to the triangle) and apply the Law of Cosines a bunch of times to find it after assuming that the system has 3-fold rotational symmetry, which works similarly well.

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- #6

Simon Bridge

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... but without seeing your working, we cannot really comment.

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