Motivated by an amazing range of reported distances to the nearby Local Group spiral galaxy M33 , we have obtained deep near-infrared photometry for 26 long-period Cepheids in this galaxy with the ESO VLT .
From the data we constructed period-luminosity relations in the J and K bands which together with previous optical VI photometry for the Cepheids by Macri et al .
were used to determine the true distance modulus of M33 , and the mean reddening affecting the Cepheid sample with the multiwavelength fit method developed in the Araucaria Project .
We find a true distance modulus of 24.62 for M33 , with a total uncertainty of \pm 0.07 mag which is dominated by the uncertainty on the photometric zero points in our photometry .
The reddening is determined as E ( B-V ) =0.19 \pm 0.02 , in agreement with the value used by the HST Key Project of Freedman et al .
but in some discrepancy with other recent determinations based on blue supergiant spectroscopy and an O-type eclipsing binary which yielded lower reddening values .
Our derived M33 distance modulus is extremely insensitive to the adopted reddening law .
We show that the possible effects of metallicity and crowding on our present distance determination are both at the 1-2 % level and therefore minor contributors to the total uncertainty of our distance result for M33 .