The Tarantula region in the Large Magellanic Cloud contains the richest population of spatially resolved massive O-type stars known so far. This unmatched sample offers an opportunity to test models describing their main-sequence evolution and mass-loss properties. Using ground-based optical spectroscopy obtained in the framework of the VLT-FLAMES Tarantula Survey (VFTS), we aim to determine stellar, photospheric and wind properties of 72 presumably single O-type giants, bright giants and supergiants and to confront them with predictions of stellar evolution and of line-driven mass-loss theories. We apply an automated method for quantitative spectroscopic analysis of O stars combining the non-LTE stellar atmosphere model {{sc fastwind}} with the genetic fitting algorithm {{sc pikaia}} to determine the following stellar properties: effective temperature, surface gravity, mass-loss rate, helium abundance, and projected rotational velocity. We present empirical effective temperature versus spectral subtype calibrations at LMC-metallicity for giants and supergiants. In the spectroscopic and classical Hertzsprung-Russell diagrams, our sample O stars are found to occupy the region predicted to be the core hydrogen-burning phase by Brott et al. (2011) and K{o}hler et al. (2015). Except for five stars, the helium abundance of our sample stars is in agreement with the initial LMC composition. The aforementioned five stars present moderate projected rotational velocities (i.e., $v_{mathrm{e}},sin,i,<,200,mathrm{km,s^{-1}}$) and hence do not agree with current predictions of rotational mixing in main-sequence stars. Adopting theoretical results for the wind velocity law, we find modified wind momenta for LMC stars that are $sim$0.3 dex higher than earlier results. [Due to the limitation of characters, the abstract appearing here is slightly shorter than that in the PDF file.]
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