Two parallel chords of a circle of radius 2 are at a distance $\sqrt{3}+1$  apart. If chords subtend at the center, angles of $\frac{\mathrm{\pi }}{\mathrm{k}}$  and  $\frac{2\mathrm{\pi }}{\mathrm{k}}$ where k>0,then the value of $\left[k\right]$ is
[Note: $\left[\mathrm{k}\right]$  denotes the largest integer less than or equal to k]