Most liquid crystals show low sensitivity to magnetic field. However, in this paper we show that a small bias magnetic field not only breaks the symmetry of the ground state, but also plays a crucial role in facilitating the reorientation induced by a large test magnetic field. In particular, a small bias field may alter significantly the strength of the test field needed to observe a given reorientation of the liquid crystal. Moreover, the bias field interacts with other symmetry breaking features of the cell, e.g., pretilt, to change also the qualitative features of the equilibrium state.