  We show that the minimal volume of surfaces of log general type, with
non-empty non-klt locus on the ample model, is $\frac{1}{825}$. Furthermore,
the ample model $V$ achieving the minimal volume is determined uniquely up to
isomorphism. The canonical embedding presents $V$ as a degree $86$ hypersurface
of $\mathbb P(6,11,25,43)$. This motivates a one-parameter deformation of $V$
to klt stable surfaces within the weighted projective space. Consequently, we
identify a $\textit{complete}$ rational curve in the corresponding moduli space
$M_{\frac{1}{825}}$.
  As an important application, we deduce that the smallest accumulation point
of the set of volumes for projective log canonical surfaces equals
$\frac{1}{825}$.
