In a $21$ sides regular polygon, how many points inside it are intersection of its diagonal?
I found that a polygon with $n$ sides has $\dfrac{n(n - 3)}{2}$ diagonals, but I feel this is not so useful to the problem solution. I've been trying for $3$ hours without success.
What's the correct solution?
This is part of a contest that is already finished (the solutions have not been released yet).