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Kosovo MO 2010 Grade 9, Problem 3

Source: Kosovo MO 2010 Grade 9, Problem 3

June 7, 2021

algebra

Problem Statement

Prove that in any polygon, there exist two sides whose radio is less than

2

.(Essentialy if

a_1\geq a_2\geq...\geq a_n

are the sides of a polygon prove that there exist

i,j\in\{1,2,..,n\}

so that

i<j

and

\frac {a_i}{a_j}<2