  The angular size of the broad line region (BLR) of the nearby active galactic
nucleus (AGN) 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 NGC3783 with an accuracy that is about a factor of two better than that
inferred from GRAVITY data alone. We derive
$M_\mathrm{BH}=2.54_{-0.72}^{+0.90}\times 10^7\,M_\odot$. Finally, and perhaps
most notably, we are able to measure a geometric distance to NGC 3783 of
$39.9^{+14.5}_{-11.9}$ 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, $H_0$, and identify
differential phase uncertainties as the current dominant limitation to the
$H_0$ measurement precision for individual sources.
