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We use the fundamental-mode RR Lyr-type variable stars (RRab) from OGLE-IVsurvey to draw a 3D picture of the central part of the tidally disruptedSagittarius Dwarf Spheroidal (Sgr dSph) galaxy. We estimate the line-of-sightthickness of the Sgr dSph stream to be FWHM_cen=2.42 kpc. Based on OGLE-IVobservations collected in seasons 2011-2014 we conduct a comprehensive study ofstellar variability in the field of the globular cluster M54 (NGC 6715)residing in the core of this dwarf galaxy. Among the total number of 268detected variable stars we report the identification of 174 RR Lyr stars, fourType II Cepheids, 51 semi-regular variable red giants, three SX Phe-type stars,18 eclipsing binary systems. Eighty-three variable stars are new discoveries.The distance to the cluster determined from RRab stars is d_M54 = 26.7+/-0.03(stat) +/-1.3(sys) kpc. From the location of RRab stars in theperiod-amplitude (Bailey) diagram we confirm the presence of two oldpopulations, both in the cluster and the Sgr dSph stream.

OGLE Study of the Sagittarius Dwarf Spheroidal Galaxy and its M54 Globular Cluster