We report the direction of tie-lines of coexisting phases in a ternary diagram of DOPC/DPPC/cholesterol lipid bilayers, which has been a system of interest in the discussion of biological rafts. For coexisting Ld and Lo phases. we find that the orientation angle a of the tie-lines increases Os the cholesterol concentration increases and it also increases as temperature increases from T = 15 degrees C to T = 30 degrees C. Results at lower cholesterol concentrations support the existence of a different two-phase coexistence region of Ld and So phases and the existence of a three-phase region separating the two two-phase regions. Our method uses the X-ray lamellar D-spacings observed in oriented bilayers as a function of varying hydration. Although this method does not obtain the ends of the tie-lines. it gives precise values (+/- 1 degrees) of their angles a in the ternary phase diagram.