  Studies of cool white dwarfs in the solar neighbourhood have placed a limit
on the age of the Galactic disk of 8-9 billion years. However, determining
their cooling ages requires the knowledge of their effective temperatures,
masses, radii, and atmospheric composition. So far, these parameters could only
be inferred for a small number of ultracool white dwarfs for which an accurate
distance is known, by fitting their spectral energy distributions (SEDs) in
conjunction with a theoretical mass-radius relation. However, the mass-radius
relation remains largely untested, and the derived cooling ages are hence
model-dependent. Here we report direct measurements of the mass and radius of
an ultracool white dwarf in the double-lined eclipsing binary SDSS
J013851.54-001621.6. We find M(WD)=0.529+/-0.010Msol and
R(WD)=0.0131+/-0.0003Rsol. Our measurements are consistent with the mass-radius
relation and we determine a robust cooling age of 9.5 billion years for the
3570K white dwarf. We find that the mass and radius of the low mass companion
star, M(sec)=0.132+/-0.003Msol and R(sec)=0.165+/-0.001Rsol, are in agreement
with evolutionary models. We also find evidence that this >9.5 Gyr old M5 star
is still active, far beyond the activity lifetime for a star of its spectral
type. This is likely caused by the high tidally-enforced rotation rate of the
star. The companion star is close to filling its Roche lobe and the system will
evolve into a cataclysmic variable in only 70 Myr. Our direct measurements
demonstrate that this system can be used to calibrate ultracool white dwarf
atmospheric models.
