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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 Nsided 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: 14,303 Thanks: 1023  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/BABYLONPROBLEM.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: 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 

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