The VISTA near-infrared Y, J, Ks survey of the Magellanic System (VMC) survey is obtaining multi-epoch photometry in the Ks band of the Magellanic System down to a limiting magnitude of Ks~19.3 for individual epoch data. The observations are spaced in time such as to provide optimal sampling of the light curves for RR Lyrae stars and for Cepheids with periods up to 20-30d. We present examples of the Ks-band light curves of Classical Cepheids and RR Lyrae stars we are obtaining from the VMC data and outline the strategy we put in place to measure distances and infer the System three-dimensional geometry from the variable stars. For this purpose, the near-infrared Period-Luminosity, Period-Wesenheit and Period-Luminosity-Colour relations of the system RR Lyrae stars and Cepheids are used. We extensively exploit the catalogues of the Magellanic Clouds' variable stars provided by the EROS-2 and OGLE III/IV microlensing surveys. By combining these surveys, we present the currently widest-area view of the Large Magellanic Cloud as captured by the galaxy Cepheids, RR Lyrae stars and binaries. This reveals the full extent of the main structures (bar/s - spiral arms) that have only been vaguely guessed before. Our work strengthens the case for a detailed study of the Large Magellanic Cloud three-dimensional geometry.