  (abridged) New photometry and spectroscopy for more than a hundred RR Lyrae
stars in two fields located close to the bar of the Large Magellanic Cloud
(LMC) are used to derive new accurate estimates of the average magnitude, the
local reddening, the luminosity-metallicity relation, and of the distance to
the LMC. Metallicities from low resolution spectra obtained with the VLT have
been derived for 101 RR Lyr's; the average value is [Fe/H]=-1.48+/-0.03
(sigma=0.29). An estimate of the reddening was obtained with 2 different
methods, and we found: E(B-V)=0.116+/-0.017, and 0.086+/-0.017 mag in field A
and B, respectively. The dereddened apparent average luminosity of the RR
Lyrae's defined by the present photometry is <V(RR)>_0=19.064+/-0.064 at
[Fe/H]=-1.5. We determine the slope of the luminosity-metallicity relation for
the RR Lyrae stars: Delta[M_V(RR)]/ Delta[Fe/H]=0.214+/-0.047, with no clear
evidence for a change in slope at [Fe/H]=-1.5. When coupled with the absolute
magnitude derived from the Baade-Wesselink and the statistical parallaxes
methods, both methods known to favour the short distance scale, this value
leads mod(LMC)=18.38+/- 0.16 and 18.30+/-0.14, respectively. If we use instead
the absolute magnitude from the new Main Sequence Fitting of Galactic globular
clusters [M_V(RR)=0.61+/-0.07 mag at [Fe/H]=-1.5] we derive
mod(LMC)=18.45+/-0.09. The average I luminosity of the clump stars is
I_0=18.12+/-0.06, and moves the clump distance modulus to the LMC to
mod(LMC)=18.42+/-0.07 and 18.45+/-0.07 when two metallicity-I relations are
used. All these values are only 1 sigma shorter than provided by the Pop I
distance indicators, and allow to reconcile the short and long distance scale
on a common value for the distance modulus of the LMC of 18.515+/-0.085 mag.
