My Math Forum Irregular polygon inscribed in a circle, find radius

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 May 10th, 2012, 07:49 AM #1 Newbie   Joined: May 2012 Posts: 4 Thanks: 0 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!
 May 10th, 2012, 08:48 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 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
 May 10th, 2012, 09:12 AM #3 Newbie   Joined: May 2012 Posts: 4 Thanks: 0 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.
 May 11th, 2012, 12:33 AM #4 Newbie   Joined: May 2012 Posts: 4 Thanks: 0 Re: Irregular polygon inscribed in a circle, find radius Well, I've gotten to this point: $\sum asin({\frac{L_{n}}{r}})=\pi$ where Ln (length of nth side) is known, but I don't know where to go from here.
 May 11th, 2012, 12:37 AM #5 Newbie   Joined: May 2012 Posts: 4 Thanks: 0 Re: Irregular polygon inscribed in a circle, find radius Sorry, that should be $\sum asin({\frac{L_{n}}{2r}})=\pi$

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equation of an irregular triangle inscribe in a circle

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