BALTIC-WAY 2024 Problem 15

There is a set of $N \geq 3$ points in the plane, such that no three of them are collinear. Three points $A$, $B, C$ in the set are said to form a Baltic triangle if no other point in the set lies on the circumcircle of triangle $A B C$. Assume that there exists at least one Baltic triangle. Show that there exist at least $\frac{N}{3}$ Baltic triangles.