Compulsory configurations of points in the plane

Let $P$ be a set of $N$ points in a general position (no three points are collinear) on the plane. A subset of $P$ may form a specific configuration, say obtuse triangle or convex pentagon. There exist configurations of points, that compulsory emerge in every point set of great enough cardinality. In this paper, such compulsory configurations of points on the plane are considered.