We consider a point $ P $ inside a regular n-gon, the distances $ a, b, c $ from the point $ P $ to $ 3 $ consecutive vertices are given and we want to find the side $ s $ of the n-gon.
If $ n = 3 $ we can calculate $ s $ as the solution of $ 3(a^4 + b^4 + c^4 + s^4) = (a^2+ b^2 + c^2 + s^2)^2 $.
If $ n ≥ 4 $ I found a formula by H . Eves ("Solution to problem 187", $ College Math. J. $, 13 (1982) , 278 – 282), but when I try to use it for simple cases it's not working, so I guess there is some sort of error. Do you know the correct formula?
