MathDB

Let

S

be a set of

2n+1

points in the plane such that no three are collinear and no four concyclic. A circle will be called

\text{Good}

if it has 3 points of

S

on its circumference,

n-1

points in its interior and

n-1

points in its exterior. Prove that the number of good circles has the same parity as

n

Problem Statement