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.
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