Let be an integer. Two regular -gons and are given in the plane. Prove that the vertices of that lie inside or on its boundary are consecutive.
(That is, prove that there exists a line separating those vertices of that lie inside or on its boundary from the other vertices of .)
Let $n\ge3$ be an integer. Two regular $n$-gons $\mathcal{A}$ and $\mathcal{B}$ are given in the plane.
Prove that the vertices of $\mathcal{A}$ that lie inside $\mathcal{B}$ or on its boundary are consecutive.
(That is, prove that there exists a line separating those vertices of $\mathcal{A}$ that lie inside $\mathcal{B}$ or on its boundary from the other vertices of $\mathcal{A}$.)
Školjka 
be an integer. Two regular 
-gons 
and 
are given in the plane. Prove that the vertices of