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Find the maximal and the minimal value of k

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 19

May 31, 2009
geometrygeometry proposed

Problem Statement

Given convex n n-gon A1…An A_1\ldots A_n. Let Pi P_i ( i \equal{} 1,\ldots , n) be such points on its boundary that AiPi A_iP_i bisects the area of polygon. All points Pi P_i don't coincide with any vertex and lie on k k sides of n n-gon. What is the maximal and the minimal value of k k for each given n n?
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