KöMaL 2015 B4703

Given that the absolute values of the numbers $x_1$, $x_2$, $x_3$, $x_4$, $x_5$, $x_6$ are at most 1, and their sum is 0, prove that $3\sum_{i=1}^{5} {\sqrt{1-x_i^2}} \le \sum_{i=1}^{5} {\sqrt{9-{(x_i+x_{i+1})}^2}}\,.$