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convex ordered polygons - Chile 2002 L2 P7

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September 1, 2022
geometrycombinatoricschilean NMO

Problem Statement

A convex polygon of sides ℓ1,ℓ2,...,ℓn\ell_1, \ell_2, ..., \ell_n is called ordered if for all reordering (σ(1),σ(2),...,σ(n))( \sigma (1), \sigma (2), ..., \sigma (n)) of the set (1,2,...,n)(1, 2,..., n) there exists a point PP inside the polygon such that dσ(1)<σ(2)<...<dσ(n)d_{\sigma (1)} < _{\sigma (2)} <...< d_{\sigma (n)} , where did_i represents the distance between PP and side ℓi\ell_i. Find all the convex ordered polygons.
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