MathDB

Let \mathcal{H} \equal{} A_1A_2\ldots A_n be a convex

n

-gon. For i \equal{} 1, 2, \ldots, n, let

A'_{i}

be the point symmetric to

A_i

with respect to the midpoint of A_{i \minus{} 1}A_{i \plus{} 1} (where A_{n \plus{} 1} \equal{} A_1). We say that the vertex

A_i

is good if

A'_{i}

lies inside

\mathcal{H}

. Show that at least n \minus{} 3 vertices of

\mathcal{H}

are good.

Problem Statement