Context : 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 .

Aims : 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 .

Methods : 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 .

Results : Our analysis indicates the presence of a point-like companion at a separation of 10.7 mas and 5.6 mag _ { K } 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 \pm 0.08 mas , corresponding to 53 \pm 3 R _ { \odot } .
at a distance of 333.3 pc .

Conclusions :