We have performed a Monte Carlo study of dimensions and intrinsic viscosities for isolated three-dimensional cyclic chains of different lengths in solution. These chains are modeled as a number of Gaussian units interacting through a 6-12 Lennard-Jones potential. The reduced energy in the potential well represents the thermodynamic quality of solvent (or the reduced inverse temperature). From this study, the Theta state for this model has been characterized. Then, transition curves and scaling plots have been obtained. Using extrapolations to the long chain limit, different conformational parameters have been estimated and compared with existing experimental data.