Question 9
Let $n\geq 6$ be an integer. In the plane there are $n$ pairwise disjoint disks $D_1,D_2,\ldots,D_n$, whose radii satisfy $r_1\geq r_2\geq\cdots\geq r_n$. For every integer $i$ with $1\leq i\leq n$, let $P_i$ be a point in the interior of $D_i$. Let $A$ be any point in the plane. Prove that
$$AP_1+AP_2+\cdots+AP_n\geq r_6+r_7+\cdots+r_n.$$
$$AP_1+AP_2+\cdots+AP_n\geq r_6+r_7+\cdots+r_n.$$