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 $rig
htarrow$ 2$alpha +$ 2emph{p}. The angular distributions and correlations of product fragments are presented for this channel. It is found that among $^{10}$C $rightarrow$ 2$alpha +$ 2emph{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.
