MathNet 2008-part-03 — 165 problems (EN–VI) Question 26

Let $A_1B_1C_1$ and $A_2B_2C_2$ be given triangles. Let $T_1$ and $T_2$ be their centers of mass, respectively. Prove that $3\overrightarrow{T_1T_2} = \overrightarrow{A_1A_2} + \overrightarrow{B_1B_2} + \overrightarrow{C_1C_2}$.