Hadrontherapy is an emerging technique in cancer therapy that uses beams of charged particles. To meet the improved capability of hadrontherapy in matching the dose release with the cancer position, new dose-monitoring techniques need to be developed and introduced into clinical use. The measurement of the fluxes of the secondary particles produced by the hadron beam is of fundamental importance in the design of any dose-monitoring device and is eagerly needed to tune Monte Carlo simulations. We report the measurements carried out with charged secondary particles produced from the interaction of a 80 MeV/u fully stripped carbon ion beam at the INFN Laboratori Nazionali del Sud, Catania, with a poly-methyl methacrylate target. Charged secondary particles, produced at 90° with respect to the beam axis, have been tracked with a drift chamber, while their energy and time of flight have been measured by means of a LYSO scintillator. Secondary protons have been identified exploiting the energy and time-of-flight information, and their emission region has been reconstructed backtracking from the drift chamber to the target. Moreover, a position scan of the target indicates that the reconstructed emission region follows the movement of the expected Bragg peak position. Exploiting the reconstruction of the emission region, an accuracy on the Bragg peak determination in the submillimeter range has been obtained. The measured differential production rate for protons produced with E(Prod)(kin) > 83 MeV and emitted at 90° with respect to the beam line is dN(P)/(dN(C)dΩ) (E(Prod)(kin) > 83 MeV, θ = 90°) = (2.69 ± 0.08(stat) ± 0.12(sys)) × 10⁻⁴ sr⁻¹.