6.74. Find the sum of the squares of the distances from the vertices of a regular $n$-gon inscribed in a circle of radius $R$ to an arbitrary line passing through the center of the polygon.
6.74. Let $e_{1}, \ldots, e_{n}$ be vectors from the center of a given $n$-gon to its vertices; $\boldsymbol{x}$ be a unit vector perpendicular to the line $l$. The desired sum is $\sum\left(\boldsymbol{e}_{i}, \boldsymbol{x}\right)^{2}=n R^{2} / 2$ (see problem 6.73 ).