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ASU 373 All Soviet Union MO 1984 2 equilaterals and equal vectors

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July 28, 2019
geometryvectorequilaterals

Problem Statement

Given two equilateral triangles A1B1C1A_1B_1C_1 and A2B2C2A_2B_2C_2 in the plane. (The vertices are mentioned counterclockwise.) We draw vectors OA→,OB→,OC→\overrightarrow{OA}, \overrightarrow{OB}, \overrightarrow{OC}, from the arbitrary point OO, equal to A1A2→,B1B2→,C1C2→\overrightarrow{A_1A_2}, \overrightarrow{B_1B_2}, \overrightarrow{C_1C_2} respectively. Prove that the triangle ABCABC is equilateral.
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