By making use of detached eclipsing binaries with B-type components discovered by the OGLE and MACHO teams in the SMC and in the LMC, we give the value of the fractional radius above which circularization occurs. This critical radius is around 0.24-0.26, regardless of the mass, surface gravity or metallicity, and is consistent with that found by Giuricin et al. [A&A 134 (1984) 365] for galactic binaries. These empirical facts are shown to be consistent with Zahn's [A&A 41 (1975) 329] theory of tidal dissipation. As a by-product of this study, we provide approximate stellar parameters of the average component of 148 binaries in the SMC and of up to 353 binaries (some of which might be non-detached) in the LMC, under the assumption of equal components.