  We present angular diameter measurements obtained by measuring the position
of Baryon Acoustic Oscillations (BAO) in an optimised sample of galaxies from
the first three years of Dark Energy Survey data (DES Y3). The sample consists
of 7 million galaxies distributed over a footprint of 4100 deg$^2$ with $0.6 <
z_{\rm photo} < 1.1$ and a typical redshift uncertainty of $0.03(1+z)$. The
sample selection is the same as in the BAO measurement with the first year of
DES data, but the analysis presented here uses three times the area, extends to
higher redshift and makes a number of improvements, including a fully
analytical BAO template, the use of covariances from both theory and
simulations, and an extensive pre-unblinding protocol. We used two different
statistics: angular correlation function and power spectrum, and validate our
pipeline with an ensemble of over 1500 realistic simulations. Both statistics
yield compatible results. We combine the likelihoods derived from angular
correlations and spherical harmonics to constrain the ratio of comoving angular
diameter distance $D_M$ at the effective redshift of our sample to the sound
horizon scale at the drag epoch. We obtain $D_M(z_{\rm eff}=0.835)/r_{\rm d} =
18.92 \pm 0.51$, which is consistent with, but smaller than, the Planck
prediction assuming flat \lcdm, at the level of $2.3 \sigma$. The analysis was
performed blind and is robust to changes in a number of analysis choices. It
represents the most precise BAO distance measurement from imaging data to date,
and is competitive with the latest transverse ones from spectroscopic samples
at $z>0.75$. When combined with DES 3x2pt + SNIa, they lead to improvements in
$H_0$ and $\Omega_m$ constraints by $\sim 20\%$
