Question 145
Let $P$ be an interior point of a regular $n$-gon $A_1A_2\cdots A_n$; the lines $A_iP$ meet the regular $n$-gon $A_1A_2\cdots A_n$ at another point $B_i$, where $i = 1, 2, \dots, n$. Prove that
$$
\sum_{i=1}^{n} PA_i \geq \sum_{i=1}^{n} PB_i.
$$
$$
\sum_{i=1}^{n} PA_i \geq \sum_{i=1}^{n} PB_i.
$$