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May 10th, 2012, 07:49 AM   #1
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Irregular polygon inscribed in a circle, find radius

Hi all,

I have the following problem. An irregular N-sided polygon is inscribed in a circle, so that each vertex lies on the circle. The length of each side of the polygon is known. How do I find the radius of the circle?

Thanks for your attention!
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May 10th, 2012, 08:48 AM   #2
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Re: Irregular polygon inscribed in a circle, find radius

Well, joining each point on circumference to center creates n isosceles triangles...

http://www2.mae.ufl.edu/~uhk/BABYLON-PROBLEM.pdf

Hope that's enough
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May 10th, 2012, 09:12 AM   #3
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Re: Irregular polygon inscribed in a circle, find radius

Thanks. I had already found that link, but this is sufficiently different from the Babylonian problem that the solutions there don't help much. Some background - I'm writing a layout algorithm for a special kind of graph, and this shape would improve efficiency a bit. Unfortunately, I haven't done trig since high school and I'm kinda short on time. I hoped someone on this board just knew the solution.
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May 11th, 2012, 12:33 AM   #4
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Re: Irregular polygon inscribed in a circle, find radius

Well, I've gotten to this point:

where Ln (length of nth side) is known, but I don't know where to go from here.
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May 11th, 2012, 12:37 AM   #5
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Re: Irregular polygon inscribed in a circle, find radius

Sorry, that should be
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