The angular size of the broad line region (BLR) of the nearby active galactic nucleus NGC 3783 has been spatially resolved by recent observations with VLTI/GRAVITY. A reverberation mapping (RM) campaign has also recently obtained high quality light curves and measured the linear size of the BLR in a way that is complementary to the GRAVITY measurement. The size and kinematics of the BLR can be better constrained by a joint analysis that combines both GRAVITY and RM data. This, in turn, allows us to obtain the mass of the supermassive black hole in NGC 3783 with an accuracy that is about a factor of two better than that inferred from GRAVITY data alone. We derive MBH = 2.54−0.72+0.90 × 107 M⊙. Finally, and perhaps most notably, we are able to measure a geometric distance to NGC 3783 of 39.9−11.9+14.5 Mpc. We are able to test the robustness of the BLR-based geometric distance with measurements based on the Tully-Fisher relation and other indirect methods. We find the geometric distance is consistent with other methods within their scatter. We explore the potential of BLR-based geometric distances to directly constrain the Hubble constant, H0, and identify differential phase uncertainties as the current dominant limitation to the H0 measurement precision for individual sources.