Let $n$ and $c$ be coprime positive integers. For any integer $i$, denote by $i' $ the remainder of division of product $ci$ by $n$. Let $A_o.A_1,A_2,...,A_{n-1}$ be a regular $n$-gon. Prove that a) if $A_iA_j \parallel A_kA_i$ then $A_{i'}A_{j'} \parallel A_{k'}A_{i'}$ b) if $A_iA_j \perp A_kA_l$ then $A_{i'}A_{j'} \perp A_{k'}A_{l'}$