  Geometry of relativistic jets in active galaxies provides important
information about mechanisms of launching, collimation and acceleration of
plasma flow. We propose a new method to probe a boundary shape of a jet on
parsec scales -- in the vicinity of its radio core. Apparent speed of an
outflow is derived from variability time delays and core shifts measured at the
same jet region, providing a self-consistent estimate of the Lorentz factor
$\Gamma$. We link together the distance along the jet $z$ with its transverse
size assuming a constant flow acceleration. Our results indicate that jets have
parabolic shape and sustain an effective acceleration in the core region,
consistent with the Lorentz factor dependency $\Gamma\propto z^{0.5}$. The
proposed method can be applied to the sources observed at small viewing angles
as well as to the distant sources when direct measurements are impossible due
to a limited angular resolution.
