A sample of 542 eclipsing binaries (EBs) with periods shorter than 2 d were selected from the Microlensing Observations in Astrophysics (MOA) EB catalogue (Li et al. 2017) for eclipse-time variation analysis. For this sample we were able to obtain the time series from MOA-II that span 9.5yr. We discovered 91 EBs, out of the 542 EBs, with detected light-travel-time effect signals suggesting the presence of tertiary companions of orbiting periods from 250 d-28 yr. The frequency of EBs with tertiary companions in our sample increases as the period decreases and reaches a value of 0.65 for contact binaries with periods shorter than 0.3 d. If only the contact binaries of periods < 0.26d are considered, the frequency even goes to the unit. Our results suggest that contact binaries with periods close to the 0.22-d contact binary limit are commonly accompanied by relatively close tertiary companions.
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