Question 8
G2 (JAP). A circle is called a separator for a set of five points in a plane if it passes through three of these points, it contains a fourth point in its interior, and the fifth point is outside the circle.
Prove that every set of five points such that no three are collinear and no four are concyclic has exactly four separators.
Prove that every set of five points such that no three are collinear and no four are concyclic has exactly four separators.