The distance to the Fornax dwarf galaxy using red clump stars, and the discrepancy between red clump and tip of the red giant branch distances

I determine a distance to the Fornax dwarf galaxy using stars in the red clump and at the tip of the red giant branch. They are in very good agreement, with $mu_0 = 20.66 mag$. Comparing the magnitudes of the tip of the red giant branch and of the red clump in Fornax, Carina and the Magellanic Clouds, I propose a possible solution to the problem of the discrepancy between these two types of distance measurements.