Proton magnetic resonance spectra of 1,3,5-tribromobenzene (TBB) and 1,3,5-trichlorobenzene (TCB) which have C 3 v symmetry were measured in a cyano-biphenyl nematic phase, with a small amount of cholesterylnonanoate added to induce a spiral-like mesophase. Depending on temperature, gradual line broadening is observed in the central signal in the triples of TBB and TCB as well as the outside signals. The broad central signal has a peak at each end of the signal in which the higher-field peak is more intense than the lower. It is found that the unsymmetrical doublet of the central signal of the C 3 v spin system is brought about by the director distribution which is neither completely nematic nor completely spiral. The unsymmetrical doublet may enable us to determine the sign of the chemical shielding anisotropy relative to the sign of the order parameter of the C 3 v spin system from measurements of the relative intensities between two peaks in the doublet. Assuming a director distribution, the chemical shielding anisotropies of TBB and TCB are estimated to be about 4 ppm smaller than those reported previously.