Question 44
In the plane there are $n\ge6$ pairwise disjoint disks $D_1,\ldots,D_n$ with radii $R_1\ge R_2\ge\cdots\ge R_n$. For each $i$, a point $P_i$ is chosen in $D_i$. Let $O$ be any point in the plane. Prove that
$$
\sum_{i=1}^{n}OP_i\ge\sum_{j=6}^{n}R_j.
$$
A disk is assumed to include its boundary.
$$
\sum_{i=1}^{n}OP_i\ge\sum_{j=6}^{n}R_j.
$$
A disk is assumed to include its boundary.