We quadruple the number of quasars known behind the Large Magellanic Cloud (LMC) from 55 (42 in the LMC fields of the third phase of the Optical Gravitational Lensing Experiment (OGLE)) to 200 by spectroscopically confirming 169 (144 new) quasars from a sample of 845 observed candidates in four ~3 deg^2 Anglo-Australian Telescope/AAOmega fields south of the LMC center. The candidates were selected based on their Spitzer mid-infrared colors, X-ray emission, and/or optical variability properties in the database of the OGLE microlensing survey. The contaminating sources can be divided into 115 young stellar objects (YSOs), 17 planetary nebulae (PNe), 39 Be and 24 blue stars, 68 red stars, and 12 objects classed as either YSO/PN or blue star/YSO. There are also 402 targets with either featureless spectra or too low signal-to-noise ratio for source classification. Our quasar sample is 50% (30%) complete at I = 18.6 mag (19.3 mag). The newly discovered active galactic nuclei (AGNs) provide many additional reference points for proper motion studies of the LMC, and the sample includes 10 bright AGNs (I < 18 mag) potentially suitable for absorption line studies. Their primary use, however, is for detailed studies of quasar variability, as they all have long-term, high cadence, continuously growing light curves from the microlensing surveys of the LMC. Completing the existing Magellanic Quasars Survey fields in the LMC and Small Magellanic Cloud should yield a sample of ~700 well-monitored AGNs, and expanding it to the larger regions covered by the OGLE-IV survey should yield a sample of ~3600 AGNs.
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