Question 95
Let $S=\{P_1,P_2,\ldots,P_{2000}\}$ be a set of $2000$ points inside a circle of radius $1$, one of which is the center. For $i=1,2,\ldots,2000$, let $x_i$ be the distance from $P_i$ to the nearest other point $P_j\in S$. Prove that
$$x_1^2+x_2^2+\cdots+x_{2000}^2\lt 9.$$
$$x_1^2+x_2^2+\cdots+x_{2000}^2\lt 9.$$