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Areas inside convex polygon

Source: Cono Sur Olympiad 2017, problem 2

August 17, 2017
geometrycono sur

Problem Statement

Let A(XYZ)A(XYZ) be the area of the triangle XYZXYZ. A non-regular convex polygon P1P2…PnP_1 P_2 \ldots P_n is called guayaco if exists a point OO in its interior such that A(P1OP2)=A(P2OP3)=⋯=A(PnOP1).A(P_1OP_2) = A(P_2OP_3) = \cdots = A(P_nOP_1). Show that, for every integer n≥3n \ge 3, a guayaco polygon of nn sides exists.
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