CONO-SUR 2017 Problem 2

Let $A(XYZ)$ be the area of the triangle $XYZ$ . A non-regular convex polygon $P_1 P_2 \ldots P_n$ is called guayaco if exists a point $O$ in its interior such that $$A(P_1OP_2) = A(P_2OP_3) = \cdots = A(P_nOP_1).$$ Show that, for every integer $n \ge 3$ , a guayaco polygon of $n$ sides exists.