Question 82
Let $P$ and $P'$ be two unequal regular $n$-gons and $A$ and $A'$ two points inside $P$ and $P'$, respectively. Suppose $\{d_1, d_2, \dots, d_n\}$ are the distances from $A$ to the vertices of $P$ and $\{d'_1, d'_2, \dots, d'_n\}$ are the distances from $A'$ to the vertices of $P'$. Is it possible for $\{d'_1, d'_2, \dots, d'_n\}$ to be a permutation of $\{d_1, d_2, \dots, d_n\}$?