Triangles in the Plane Containing a Point
Source: 2017 Greece National Olympiad Problem 2
May 2, 2017
combinatorics
Problem Statement
Let be a point in the plane and lines which pass through this point divide the plane in regions.
In each region there are points. We know that no three of the points existing in these regions are collinear. Prove that there exist at least triangles whose vertices are points of those regions such that lies either in the interior or on the side of the triangle.