The eigenvalues of the distance matrix $D-$ of a graph $G$ forms the distance spectrum, $D-$ spectrum of $G$. Distance energy $E_D$, of a graph~$G$ is one of the recent energy-type invariants, defined as the absolute deviation of the eigenvalues of the distance matrix of $G$. In this paper the $D-$ spectrum and energy of the median and total graph of a cycle are obtained.