Let $A=\{P_1,P_2,…,P_{2011}\}$ be a set of points that lie in a circle $K(P_1,1)$. With $x_k$ we denote the distance between $P_k$ and the closest to it point from $A$. Prove that: $\sum_{i=1}^{2011} x_i^2 \leq \frac{9}{4}$.