Following the recommendation of the European Strategy Group for Particle Physics, the Future Circular Collider (FCC) study was launched by CERN to investigate circular collider designs for a post-LHC era. Among the studied collider designs is a hadron-collider option aiming to collide protons at a center of mass energy of 100 TeV. This hadron collider option (FCC-hh) follows a similar layout as the LHC with two high luminosity experimental insertions, meant to complement each other and two low luminosity experiments. This thesis studies the option of combining these low luminosity experiments with the injection in the FCC-hh. Using a contrary design approach to the combined insertion in the LHC and taking into account the constraint from the injection a layout was developed. The goal when developing the beam optics for the insertion was to achieve the lowest possible beam size in the interaction point to guarantee a high event rate. Furthermore, the impact of magnetic field errors in the magnets of this insertion on the beam stability was studied and are discussed in this thesis. In addition, a possible strategy is then presented which would allow to further increase the event rate.