The interaction position resolution of the segmented HPGe detectors of an AGATA triple cluster detector has been studied through Monte Carlo simulations and in an in-beam experiment. A new method based on measuring the energy resolution of Doppler-corrected γ-ray spectra at two different target to detector distances is described. This gives the two-dimensional position resolution in the plane perpendicular to the direction of the emitted γ-ray. The γ-ray tracking was used to determine the full energy of the γ-rays and the first interaction point, which is needed for the Doppler correction. Five different heavy-ion induced fusion-evaporation reactions and a reference reaction were selected for the simulations. The results of the simulations show that the method works very well and gives a systematic deviation of View the MathML source in the FWHM of the interaction position resolution for the γ-ray energy range from 60 keV to 5 MeV. The method was tested with real data from an in-beam measurement using a 30Si beam at 64 MeV on a thin 12C target. Pulse-shape analysis of the digitized detector waveforms and γ-ray tracking was performed to determine the position of the first interaction point, which was used for the Doppler corrections. Results of the dependency of the interaction position resolution on the γ-ray energy and on the energy, axial location and type of the first interaction point, are presented. The FWHM of the interaction position resolution varies roughly linearly as a function of γ-ray energy from 8.5 mm at 250 keV to 4 mm at 1.5 MeV, and has an approximately constant value of about 4 mm in the γ-ray energy range from 1.5 to 4 MeV.