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E_A x{OA}+E_B x {OB}+E_C x{OC}=O - Carathéodory

Source: 1985 Greece MO Grade XII p1

September 6, 2024
geometryvectorareasanalytic geometry

Problem Statement

Inside triangle ABCABC consider random point OO. Prove that: EAOA→+EBOB→+ECOC→=O→E_A \overrightarrow{OA}+E_B \overrightarrow{OB}+E_C\overrightarrow{OC}=\overrightarrow{O} where EA,EB,ECE_A,E_B,E_C the areas of triangle BOC,COB,AOBBOC, COB, AOB respectively
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