Question 174
Inside an equilateral triangle $ABC$ point $M$ is chosen. Let points $M_1$, $M_2$, $M_3$ be the points symmetric to $M$ with respect to the sides $BC$, $AC$, $AB$ of the triangle respectively. Prove that $\overrightarrow{MM_1} + \overrightarrow{MM_2} + \overrightarrow{MM_3}$ is equal to $\overrightarrow{MA} + \overrightarrow{MB} + \overrightarrow{MC}$.
(Tereshin Dmitro)
(Tereshin Dmitro)