2020 IMO Shortlist G4

In the plane, there are $n \geq 6$ pairwise disjoint disks $D_{1}, D_{2}, \ldots, D_{n}$ with radii $R_{1} \geq R_{2} \geq \ldots \geq R_{n}$. For every $i=1,2, \ldots, n$, a point $P_{i}$ is chosen in disk $D_{i}$. Let $O$ be an arbitrary point in the plane. Prove that $$O P_{1}+O P_{2}+\ldots+O P_{n} \geq R_{6}+R_{7}+\ldots+R_{n}$$ (A disk is assumed to contain its boundary.) (Iran)

在平面上，有 $n \geq 6$ 成对不相交圆盘 $D_{1}, D_{2}, \ldots, D_{n}$，半径为 $R_{1} \geq R_{2} \geq \ldots \geq R_{n}$。对于每个$i=1,2,\ldots,n$，在磁盘$D_{i}$中选择一个点$P_{i}$。令 $O$ 为平面上的任意点。证明 $$O P_{1}+O P_{2}+\ldots+O P_{n} \geq R_{6}+R_{7}+\ldots+R_{n}$$ (假设磁盘包含其边界。)(伊朗)