  The charge topology in the fragmentation of $^{10}$C nuclei in a track
nuclear emulsion at an energy of 1.2 GeV per nucleon is studied. In the
coherent dissociation of $^{10}$C nuclei, about 82% of events are associated
with the channel $^{10}$C $\rightarrow$ 2$\alpha +$ 2\emph{p}. The angular
distributions and correlations of product fragments are presented for this
channel. It is found that among $^{10}$C $\rightarrow$ 2$\alpha +$ 2\emph{p}
events, about 30% are associated with the process in which dissociation through
the ground state of the unstable $^9$Be$_{g.s.}$ nucleus is followed by
$^8$Be$_{g.s.} +$ \emph{p} decays.
