Plane geometry I · Chapter IV · Warm-up
Let \(T_1\) and \(T_2\) be the centroids of triangles \(A_1B_1C_1\) and \(A_2B_2C_2\), respectively. Prove that
\[ \overrightarrow{A_1A_2} + \overrightarrow{B_1B_2} + \overrightarrow{C_1C_2} = 3\,\overrightarrow{T_1T_2}. \]
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Serbian Municipal Competition 2010, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source