A plane has a special point O called the origin. Let P be a set of 2021 points in the plane such that[*] no three points in P lie on a line and
[*] no two points in P lie on a line through the origin.A triangle with vertices in P is fat if O is strictly inside the triangle. Find the maximum number of fat triangles. EGMO 2021geometrycombinatorial geometryEGMOTriangles