GAIC Math 2024 Problem 96

Known that there is a regular 200-gon $A_{1}A_{2} \ldots A_{200}$, connecting the diagonals $A_{i}A_{i+9}(\mathrm{i}=1,2, \ldots, 200)$, where $A_{i+200}=A_{i}(i=1,2, \ldots, 9)$. Then there are a total of _____ distinct intersection points inside the regular 200-gon.