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 [ \hbox { Fe / H } ] = -1.3 ( RR Lyraes ) and -1.0 ( Cepheids ) , we find a relatively steep slope of 0.34 \pm 0.20 magnitudes per dex for the RR Lyraes and a shallow slope of -0.07 \pm 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 \pm 0.06 , corresponding to a distance of 730 \pm 20 kpc .
This distance produces an RR Lyrae absolute magnitude of M _ { V } = 0.61 \pm 0.08 .