Consider a regular n-gon with side length $A$.
Let $p$ be a point in the polygon. Let the distances from $p$ to the corners of the n-gon be $x_1,x_2,...,x_n$
Are there solutions with $A,x_1,x_2,...x_n$ all positive integers and $gcd(A,x_1,x_2,...,x_n) = 1$.
For the triangle ( $n=3$) this question has been answered already here
I assume for sufficiently large $n$ there are no solutions ?
In particular im intrested in $n=4,5,6$.