2021 EGMO P5: Maximum number of fat triangles
Source: 2021 EGMO P5
April 13, 2021
EGMO 2021geometrycombinatorial geometryEGMOTriangles
Problem Statement
A plane has a special point called the origin. Let be a set of 2021 points in the plane such that[*] no three points in lie on a line and
[*] no two points in lie on a line through the origin.A triangle with vertices in is fat if is strictly inside the triangle. Find the maximum number of fat triangles.