  The new data for Cepheids and RR Lyrae stars of the Optical Gravitational
Lensing Experiment (OGLE-III) survey allow us to study the three-dimensional
distribution of stars corresponding to young (a few tens to a few hundreds of
millions of years) and old (typically older than ~9 Gyr) populations of the
Large Magellanic Cloud (LMC) traced by these variable stars. We estimate the
distance to 16949 RR Lyrae stars by using their photometrically estimated
metallicities. Furthermore the periods of 1849 Cepheids are used to determine
their distances. Three-dimensional maps are obtained by using individual
reddening estimates derived from the intrinsic color of these stars. The
resulting median distances of the RR Lyrae stars and Cepheids appear to resolve
the long and short distance scale problem for our sample. With median distances
of 53.1 \pm 3.2 kpc for the RR Lyrae stars and 53.9 \pm 1.8 kpc for the
Cepheids, these two distance indicators are in very good agreement with each
other in contrast to a number of earlier studies. Individual reddening
estimates allow us to resolve the distance discrepancies often observed while
comparing Cepheids and RR Lyrae stars. For both stellar populations we find the
inclination angle of the LMC to be 32{\deg} \pm 4{\deg} and the mean position
angle to be 115{\deg} \pm 15{\deg}. The position angle increases with
galactocentric radius, indicative of mild twisting. Within the innermost 7
degrees of the LMC covered by OGLE III the change in position angle amounts to
more than 10 degrees. The depth of the Cepheids is found to be 1.7 \pm 0.2 kpc.
The bar stands out as an overdensity both in RR Lyrae stars and in Cepheids. In
RR Lyrae stars the bar can be traced as a protruding overdensity with a
line-of-sight depth of almost 5 kpc in front of the main body of the disk.
