The Araucaria Project. On the Tip of the Red Giant Branch distance determination to the Magellanic Clouds

We present a precise optical and near-infrared determination of the Tip of the Red Giant Branch (TRGB) brightness in the Large and Small Magellanic Clouds (respectively LMC and SMC). The commonly used calibrations of the absolute magnitude of the TRGB lead to an overestimation of the distance to the LMC and SMC in the K band, and an underestimation of the distance in the optical I band for both galaxies. Reported discrepancies are at the level of 0.2 mag, with respect to the very accurate distance determinations to both Clouds based on late-type eclipsing binaries. The differential distances between the LMC and SMC obtained in the J and K bands, and for the bolometric brightness are consistent with each other, and with the results obtained from eclipsing binaries and other distance indicators.