MathDB

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}

G6