RO-TST 2012 Problem 19

Let $m$ and $n$ be two positive integers for which $m<n$ . $n$ distinct points $X_1,\ldots , X_n$ are in the interior of the unit disc and at least one of them is on its border. Prove that we can find $m$ distinct points $X_{i_1},\ldots , X_{i_m}$ so that the distance between their center of gravity and the center of the circle is at least $\frac{1}{1+2m(1- 1/n)}$ .