OBM 2006 Problem 2

Let $n$ be an integer, $n \geq 3$ . 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 $an^{2}< f(n) < bn^{2}$ for every integer $n$ , $n \geq 3$ .