We present a spectroscopic analysis of the O9.7 Iab star HDE 226868, which is the optical counterpart of Cygnus X-1. We use this extreme supergiant to test the differences in the stellar parameters derived using plane parallel hydrostatic model atmospheres and spherical non-hydrostatic models ("Unified Model"). We find that the difference is significant, but smaller than it is needed to explain the mass and helium discrepancy between the theories of stellar atmospheres and evolution. We also find that the dilution effect of HeI 4471 is not due only to the presence of a strong wind. We use the derived atmospheric parameters to show that Cygnus X-1 has to be a black hole (provided it is a single compact object) in a way that is independent of the distance to the system and assumptions about the mass-luminosity relation of the visible star. We also derive a probable mass for Cygnus X-1.