Problem

Source: Cono Sur Olympiad 2017, problem 2

Tags: geometry, cono sur



Let A(XYZ) be the area of the triangle XYZ. A non-regular convex polygon P1P2Pn is called guayaco if exists a point O in its interior such that A(P1OP2)=A(P2OP3)==A(PnOP1).Show that, for every integer n3, a guayaco polygon of n sides exists.