Question 99
Given $n$ points $P_1, P_2, \dots, P_n$ on a plane, let $M$ be any point on segment $AB$ on the plane. Denote by $|P_iM|$ the distance between $P_i$ and $M$, $i = 1, 2, 3, \dots, n$. Prove that
$$
\sum_{i=1}^n |P_iM| \le \max\left\{\sum_{i=1}^n |P_iA|, \sum_{i=1}^n |P_iB|\right\}.
$$
(posed by Jin Mengwei)
$$
\sum_{i=1}^n |P_iM| \le \max\left\{\sum_{i=1}^n |P_iA|, \sum_{i=1}^n |P_iB|\right\}.
$$
(posed by Jin Mengwei)