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Problem 2 of First round

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 13, 2019
geometryoctagonVectorsvector

Problem Statement

Let A1A2A3A4A5A6A7A8A_1A_2A_3A_4A_5A_6A_7A_8 be a right octagon with center OO and λ1\lambda_1,λ2\lambda_2, λ3\lambda_3, λ4\lambda_4 be some rational numbers for which: λ1OA1→+λ2OA2→+λ3OA3→+λ4OA4→=o→\lambda_1 \overrightarrow{OA_1}+\lambda_2 \overrightarrow{OA_2}+\lambda_3 \overrightarrow{OA_3}+\lambda_4 \overrightarrow{OA_4} =\overrightarrow{o}. Prove that λ1=λ2=λ3=λ4=0\lambda_1=\lambda_2=\lambda_3=\lambda_4=0.
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