  Exact mathematical identities are presented between the relevant parameters
of droplets displaying circular contact boundary based on flat tilted surfaces.
Two of the identities are derived from the force balance, and one from the
torque balance. The tilt surfaces cover the full range of inclinations for
sessile or pendant drops, including the intermediate case of droplets on a wall
(vertical surface). The identities are put under test both by the available
solutions of a linear response approximation at small Bond numbers as well as
the ones obtained from numerical solutions, making use of the Surface Evolver
software. The subtleties to obtain certain angle-averages appearing in
identities by the numerical solutions are discussed in detail. It is argued how
the identities are useful in two respects. First is to replace some unknown
values in the Young-Laplace equation by their expressions obtained from the
identities. Second is to use the identities to estimate the error for
approximate analytical or numerical solutions without any reference to an exact
solution.
