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sum of altitude vectors is zero, then triangle is equilateral

Source: Croatia 1998 3rd Grade P3

June 8, 2021
vectorgeometryTriangles

Problem Statement

Let AA1,BB1,CC1AA_1,BB_1,CC_1 be the altitudes of a triangle ABCABC. If AA1→+BB1→+CC1→=0\overrightarrow{AA_1}+\overrightarrow{BB_1}+\overrightarrow{CC_1}=0 prove that the triangle ABCABC is equilateral.
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