  The first secant variety $\Sigma$ of a rational normal curve of degree $d
\geq 3$ is known to be a $\mathbf{Q}$-Fano threefold. In this paper, we prove
that $\Sigma$ is K-polystable, and hence, $\Sigma$ admits a weak
K\"{a}hler-Einstein metric. We also show that there exists a
$(-K_{\Sigma})$-polar cylinder in $\Sigma$.
