Given convex $1000$-gon. Inside this polygon, $1020$ points are chosen so that no $3$ of the $2020$ points do not lie on one line. Polygon is cut into triangles so that these triangles have vertices only those specified $2020$ points and each of these points is the vertex of at least one of cutting triangles. How many such triangles were formed?
Problem
Source: December 2020 Ukraine Geometry Olympiad IX p3
Tags: geometry, combinatorics, combinatorial geometry