We analyze the mean luminosity of three samples of field RRab Lyr stars observed in the course of the OGLE microlensing experiment: 73 stars from the Galactic bulge and 110 and 128 stars from selected fields in the LMC and SMC, respectively. The fields are the same as in the recent distance determination to the Magellanic Clouds with the red clump stars method by Udalski et al. (1998). We determine the relative distance scale dGBRR:dLMCRR:dSMCRR equal to: (0.194 +/- 0.010):1.00:(1.30 +/- 0.08). We calibrate our RR Lyr distance scale with the recent calibration of Gould and Popowski (1998) based on statistical parallaxes. We obtain the following distance moduli to the Galactic bulge, LMC and SMC: m-M=14.53 +/- 0.15, m-M=18.09 +/- 0.16 and m-M=18.66 +/- 0.16 mag. We use the RR Lyr mean V-band luminosity at the Galactic bulge metallicity as the reference brightness and analyze the mean, I-band luminosity of the red clump stars in objects with different ages and metallicities. We add to our analysis the metal poor Carina dwarf galaxy which contains old RR Lyr stars and intermediate age red clump population. We find a weak dependence of the mean red clump brightness on metallicity and we calibrate its zero point with the nearby local red clump stars measured by Hipparcos: MRC_I=(0.09 +/- 0.03) times [Fe/H]RC-0.23 +/- 0.03. Our revised red clump distance moduli to the Galactic bulge, LMC and SMC are m-M=14.53 +/- 0.06, m-M=18.13 +/- 0.07 and m-M=18.63 +/- 0.07 mag, respectively. The distance modulus to the Carina galaxy is m-M=19.84 +/- 0.07 mag. Excellent agreement of RR Lyr and red clump distance s which have independent absolute calibrations confirms the short distance scale to the LMC.