Measuring the proper motions and geometric distances of galaxies within the Local Group is very important for our understanding of the history, present state and future of the Local Group. Currently, proper motion measurements using optical methods are limited only to the closest companions of the Milky Way. However, Very Long Baseline Interferometry (VLBI) provides the best angular resolution in astronomy and phase-referencing techniques yield astrometric accuracies of ≈ 10 micro-arcseconds. This makes a measurement of proper motions and angular rotation rates of galaxies out to a distance of ∼ 1 Mpc feasible. This article presents results of VLBI observations of regions of H2O maser activity in the Local Group galaxies M33 and IC 10. Two masing regions in M33 are on opposite sides of the galaxy. This allows a comparison of the angular rotation rate (as measured by the VLBI observations) with the known inclination and rotation speed of the HI gas disk. This gives a geometric distance of 730 ± 100 ± 135 kpc. The first error indicates the statistical error from the proper motion measurements while the second error is the systematic error from the rotation model. This distance is consistent, within the errors, with the most recent Cepheid distance to M33. Since all position measurements were made relative to an extragalactic background source, the proper motion o
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