We present color-magnitude diagrams and luminosity functions of stars in the nearby galaxy IC 10 , based on VI CCD photometry acquired with the COSMIC prime-focus camera on the Palomar 5m telescope .
The apparent I-band luminosity function of stars in the halo of IC 10 shows an identifiable rise at I \approx 21.7 mag .
This is interpreted as being the tip of the red giant branch ( TRGB ) at M _ { V } \approx -4 mag .
Since IC 10 is at a very low Galactic latitude , its foreground extinction is expected to be high and the uncertainty associated with that correction is the largest contributor to the error associated with its distance determination .
Multi-wavelength observations of Cepheid variable stars in IC 10 give a Population I distance modulus of 24.1 \pm 0.2 mag , which corresponds to a linear distance of 660 \pm 66 kpc for a total line-of-sight reddening of E ( B-V ) = 1.16 \pm 0.08 mag , derived self-consistently from the Cepheid data alone .
Applying this Population I reddening to the Population II halo stars gives a TRGB distance modulus of 23.5 \pm 0.2 mag , corresponding to 500 \pm 50 kpc .
We consider this to be a lower limit on the TRGB distance .
Reconciling the Cepheid and TRGB distances would require that the reddening to the halo is \Delta E ( B-V ) = 0.31 mag lower than that into the main body of the galaxy .
This then suggests that the Galactic extinction in the direction of IC 10 is E ( B - V ) \simeq 0.85 .