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For every pair, there exists a point that makes 60 degrees

Source: 2012 Indonesia Round 2.5 TST 4 Problem 3

May 31, 2012
geometry unsolvedgeometry

Problem Statement

Let P1P2…PnP_1P_2\ldots P_n be an nn-gon such that for all i,j∈{1,2,…,n}i,j \in \{1,2,\ldots,n\} where i≠ji \neq j, there exists k≠i,jk \neq i,j such that ∠PiPkPj=60∘\angle P_iP_kP_j = 60^\circ. Prove that n=3n=3.
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