  We present WFPC2 VI photometry of a field in the halo of IC 1613, finding 13
RR Lyraes and 11 Cepheids. Our photometry of the red giant branch tip and red
clump is used to derive distances to IC 1613, which are consistent with each
other and with distances based on the variable stars. We compare these values
with similarly-measured distances for the Magellanic Clouds, and are able to
measure metallicity dependencies of the RR Lyrae and Cepheid distances by
requiring consistent relative distance measurements from the four techniques.
For metallicities of [Fe/H] = -1.3 (RR Lyraes) and -1.0 (Cepheids), we find a
relatively steep slope of 0.34 +/- 0.20 magnitudes per dex for the RR Lyraes
and a shallow slope of -0.07 +/- 0.16 mag/dex for the Cepheids, both values
within the range of theoretical and empirical results in the literature. We
find that a dependence of the red clump absolute magnitude on age, in addition
to metallicity, is required to produce self-consistent relative distances
between IC 1613 and the Magellanic Clouds. Adopting such a red clump
calibration and self-consistent calibrations for the other three distance
indicators, we find that the distances to all three objects are in excellent
agreement. Our best distance modulus to IC 1613 is mu_0 = 24.31 +/- 0.06,
corresponding to a distance of 730 +/- 20 kpc. This distance produces an RR
Lyrae absolute magnitude of MV = 0.61 +/- 0.08.
