Hi people! Need help with this question...(Smirk)

Let A1, A2, ... A200 be a regular 200-sided convex polygon. Make the diagonals AiAi+9, i = 1, 2, ...., 200, where Ai+200 = Ai for 1<i<9. How many distinct points of intersection are formed inside the polygon by these 200 diagonals?