  We derive an analytic solution for the minimization problem in the geometric
Baade-Wesselink method. This solution allows deriving the distance and mean
radius of a pulsating star by fitting its velocity curve and angular diameter
measured interferometrically. The method also provide analytic solutions for
the confidence levels of the best fit parameters, and accurate error estimates
for the Baade-Wesselink solution. Special care is taken in the analysis of the
various error sources in the final solution, among which the uncertainties due
to the projection factor, the limb darkening and the velocity curve. We also
discuss the importance of the phase shift between the stellar lightcurve and
the velocity curve as a potential error source in the geometric Baade-Wesselink
method. We finally discuss the case of the Classical Cepheid zeta Gem, applying
our method to the measurements derived with the Palomar Testbed Interferometer.
We show how a careful treatment of the measurement errors can be potentially
used to discriminate between different models of limb darkening using
interferometric techniques.
