  We report estimates of the X-ray coronal size of active galactic nuclei in
the lamppost geometry. In this commonly adopted scenario, the corona is assumed
for simplicity to be a point-like X-ray source located on the axis of the
accretion disc. However, the corona must intercept a number of optical/UV seed
photons from the disc consistent with the observed X-ray flux, which constrains
its size. We employ a relativistic ray-tracing code, originally developed by
Dov\v{c}iak & Done (2016), that calculates the size of a Comptonizing lamppost
corona illuminated by a standard thin disc. We assume that the disc extends
down to the innermost stable circular orbit of a non-spinning or a maximally
spinning black hole. We apply this method to a sample of 20 Seyfert 1 galaxies,
using simultaneous optical/UV and X-ray archival data from XMM-Newton. At least
for the sources accreting below the Eddington limit, we find that a
Comptonizing lamppost corona can generally exist, but with constraints on its
size and height above the event horizon of the black hole depending on the
spin. For a maximally spinning black hole, a solution can almost always be
found at any height, while for a non-spinning black hole the height must
generally be higher than 5 gravitational radii. This is because, for a given
luminosity, a higher spin implies more seed photons illuminating the corona due
to a larger and hotter inner disc area. The maximal spin solution is favored,
as it predicts an X-ray photon index in better agreement with the observations.
