We have developed a strategy to determine lengths and orientations of tie lines in the coexistenceregion of liquid-ordered and liquid-disordered phases of cholesterol containing ternary lipid mixtures. The method combines confocal-fluorescence-microscopy image stacks of giant unilamellar vesicles (GUVs), a dedicated 3D-image analysis and a quantitative analysis based in equilibrium thermodynamic considerations. This approach was tested in GUVs composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine/1,2-palmitoyl-sn-glycero-3-phosphocholine/cholesterol. In general, our results show a reasonable agreement with previously reported data obtained by other methods. For example, our computed tie lines were found to be nonhorizontal, indicating a difference in cholesterol content in the coexisting phases. This new, to our knowledge, analytical strategy offers a way to further exploit fluorescence-microscopy experiments in GUVs, particularly retrieving quantitative data for the construction of three lipid-component-phase diagrams containing cholesterol.