  We have used the infrared Barnes-Evans surface brightness technique to derive
the radii and distances of 34 Galactic Cepheid variables. Radius and distance
results obtained from both versions of the technique are in excellent
agreement. The radii of 28 variables are used to determine the period-radius
relation. This relation is found to have a smaller dispersion than in previous
studies, and is identical to the period-radius relation found by Laney & Stobie
from a completely independent method, a fact which provides persuasive evidence
that the Cepheid period-radius relation is now determined at a very high
confidence level. We use the accurate infrared distances to determine
period-luminosity relations in the V, I, J, H and K passbands from the Galactic
sample of Cepheids. We derive improved slopes of these relations from updated
LMC Cepheid samples and adopt these slopes to obtain accurate absolute
calibrations of the PL relation. By comparing these relations to the ones
defined by the LMC Cepheids, we derive strikingly consistent and precise values
for the LMC distance modulus in each of the passbands which yield a mean value
of DM (LMC) = 18.46 +- 0.02.
  Our results show that the infrared Barnes-Evans technique is very insensitive
to both Cepheid metallicity and adopted reddening, and therefore a very
powerful tool to derive accurate distances to nearby galaxies by a direct
application of the technique to their Cepheid variables, rather than by
comparing PL relations of different galaxies, which introduces much more
sensitivity to metallicity and absorption corrections which are usually
difficult to determine.
