  OGLE-LMC-DPV-065 is an interacting binary whose double-hump long photometric
cycle remains hitherto unexplained. We analyze photometric time series
available in archive datasets spanning 124 years and present the analysis of
new high-resolution spectra. A refined orbital period is found of 10\fd0316267
$\pm$ 0\fd0000056 without any evidence of variability. In spite of this
constancy, small but significant changes in timings of the secondary eclipse
are detected. We show that the long period continuously decreases from 350 to
218 days during 13 years, then remains almost constant for about 10 years. Our
study of radial velocities indicates a circular orbit for the binary and yields
a mass ratio of 0.203 $\pm$ 0.001. From the analysis of the orbital light curve
we find that the system contains 13.8 and 2.81 \msun\ stars of radii 8.8 and
12.6 \rsun\ and absolute bolometric magnitudes -6.4 and -3.0, respectively. The
orbit semi-major axis is 49.9 \rsun\ and the stellar temperatures are 25460 K
and 9825 K. We find evidence for an optically and geometrically thick disk
around the hotter star. According to our model, the disk has a radius of 25
\rsun, central and outer vertical thickness of 1.6 \rsun\ and 3.5 \rsun, and
temperature of 9380 K at its outer edge. Two shock regions located at roughly
opposite parts of the outer disk rim can explain the light curves asymmetries.
The system is a member of the double periodic variables and its relatively
high-mass and long photometric cycle make it similar in some aspects to $\beta$
Lyrae.
