JMO 1991 Problem 5

Let $A$ be a set of $n\geq 2$ points on a plane. Prove that there exists a circle which contains at least $\left[\frac{n}{3}\right]$ points of $A$ among circles (involving perimeter) with some end points taken from $A$ as the diameter, where $[x]$ is the greatest integer which is less than or equal to $x$.