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vectorial geometry

Source: Romanian District Olympiad, Grade IX, Problem 4

September 24, 2018
geometrycontestsOlympiad

Problem Statement

Let be a circle centeted at O, O, and A,B,C, A,B,C, points situated on this circle. Show that if ∣OA→+OB→∣=∣OB→+OC→∣=∣OC→+OA→∣, \left|\overrightarrow{OA} +\overrightarrow{OB}\right| = \left|\overrightarrow{OB} +\overrightarrow{OC}\right| = \left|\overrightarrow{OC} +\overrightarrow{OA}\right| , then A=B=C, A=B=C, or ABC ABC is an equilateral triangle.
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