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The determination of the size and geometry of the broad line region (BLR) in active galactic nuclei is one of the major ingredients for determining the mass of the accreting black hole. This can be done by determining the delay between the optical continuum and the flux reprocessed by the BLR, in particular via the emission lines. We propose here that the delay between polarized and unpolarized light can also be used in much the same way to constrain the size of the BLR; we check that meaningful results can be expected from observations using this technique. We use our code STOKES for performing polarized radiative transfer simulations. We determine the response of the central source environment (broad line region, dust torus, polar wind) to fluctuations of the central source that are randomly generated; we then calculate the cross correlation between the simulated polarized flux and the total flux to estimate the time delay that would be provided by observations using the same method. We find that the broad line region is the main contributor to the delay between the polarized flux and the total flux; this delay is independent on the observation wavelength. This validates the use of polarized radiation in the optical/UV band to estimate the geometrical properties of the broad line region in type I AGNs, in which the viewing angle is close to pole-on and the BLR is not obscured by the dust torus.