Optical-infrared interferometry can provide direct geometrical measurements of the radii of Cepheids and/or reveal unknown binary companions of these stars. Such information is of great importance for a proper calibration of Period-Luminosity relations and for determining binary fraction among Cepheids. We observed the Cepheid X Sgr with VLTI/AMBER in order to confirm or disprove the presence of the hypothesized binary companion and to directly measure the mean stellar radius, possibly detecting its variation along the pulsation cycle. From AMBER observations in MR mode we performed a binary model fitting on the closure phase and a limb-darkened model fitting on the visibility. Our analysis indicates the presence of a point-like companion at a separation of 10.7 mas and 5.6 magK fainter than the primary, whose flux and position are sharply constrained by the data. The radius pulsation is not detected, whereas the average limb-darkened diameter results to be 1.48+/-0.08 mas, corresponding to 53+/-3 R_sun at a distance of 333.3 pc.
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