RU-ALLRUSSIAN 1969 Problem 13

A regular n- gon is inscribed in a circle radius R. The distance from the center of the circle to the center of a side is $\mathbf{h}_{\mathrm{n}}$ . Prove that $(n + 1) \mathbf{h}_{\mathrm{n} + 1} - \mathbf{n} \mathbf{h}_{\mathrm{n}} > \mathbf{R}$ .