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We present the results of a study of the type II Cepheid ($P_{puls} = 4.974d$) in the eclipsing binary system OGLE-LMC-T2CEP-098 ($P_{orb} = 397.2 d$).The Cepheid belongs to the peculiar W Vir group, for which the evolutionarystatus is virtually unknown. It is the first single-lined system with apulsating component analyzed using the method developed by Pilecki et al.(2013). We show that the presence of a pulsator makes it possible to deriveaccurate physical parameters of the stars even if radial velocities can bemeasured for only one of the components. We have used four different methods tolimit and estimate the physical parameters, eventually obtaining preciseresults by combining pulsation theory with the spectroscopic and photometricsolutions. The Cepheid radius, mass and temperature are $25.3 \pm 0.2 R_\odot$,$1.51 \pm 0.09 M_\odot$ and $5300 \pm 100 K$, respectively, while its companionhas similar size ($26.3 R_\odot$), but is more massive ($6.8 M_\odot$) andhotter ($9500 K$). Our best estimate for the p-factor of the Cepheid is $1.30\pm 0.03$. The mass, position on the period-luminosity diagram, and pulsationamplitude indicate that the pulsating component is very similar to theAnomalous Cepheids, although it has a much longer period and is redder incolor. The very unusual combination of the components suggest that the systemhas passed through a mass transfer phase in its evolution. More complicatedinternal structure would then explain its peculiarity.

Mass and p-factor of the type II Cepheid OGLE-LMC-T2CEP-098 in a binary system