10.8 Suppose $S$ is a set of points in the plane, $|S|$ is even; no three points of $S$ are collinear. Prove that $S$ can be partitioned into two sets $S_1$ and $S_2$ so that their convex hulls have equal number of vertices.
Source: Sharygin 2017 Day 2 Problem 10.8 Grade 10
Tags: geometry
10.8 Suppose $S$ is a set of points in the plane, $|S|$ is even; no three points of $S$ are collinear. Prove that $S$ can be partitioned into two sets $S_1$ and $S_2$ so that their convex hulls have equal number of vertices.