Question 198
Let $n$ be an integer, $n \ge 3$. Let $f(n)$ be the largest number of isosceles triangles whose vertices belong to some set of $n$ points in the plane without three colinear points. Prove that there exists positive real constants $a$ and $b$ such that $an^2 \lt f(n) \lt bn^2$ for every integer $n$, $n \ge 3$.