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

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