MathDB

4

Part of 2000 Romania Team Selection Test

Problems(1)

N-gon must be a triangle if always exists a 60 degree angle

Source: Romanian TST 2000

2/14/2011
Let P1P2…PnP_1P_2\ldots P_n be a convex polygon in the plane. We assume that for any arbitrary choice of vertices Pi,PjP_i,P_j there exists a vertex in the polygon PkP_k distinct from Pi,PjP_i,P_j such that ∠PiPkPj=60∘\angle P_iP_kP_j=60^{\circ}. Show that n=3n=3.
Radu Todor
geometrycombinatorics unsolvedcombinatorics