  Active galactic nucleus (AGN) feedback provides the link between the central
black hole and its host galaxy. We assume AGN feedback driven by radiation
pressure on dust, which sweeps up the ambient dusty gas into an outflowing
shell, and consider feedback-triggered star formation in the outflow. An upper
limit to the characteristic size of galaxies may be defined by the critical
radius beyond which radiation pressure on dust is no longer able to drive the
shell. The corresponding enclosed mass may be compared with the host galaxy
bulge mass. We show that the resulting relation between characteristic radius
and mass, of the form $R \propto \sqrt M$, corresponds to the observed
mass-radius relation of early-type galaxies. We suggest that such simple
physical scalings may account for a number of observed galaxy scaling
relations. In this picture, both the size and structural evolution of galaxies
can be interpreted as a consequence of AGN feedback-driven star formation,
mainly associated with the spheroidal component. The accreting black hole is
responsible for triggering star formation in the host galaxy, while ultimately
clearing the dusty gas out of the host, thus also contributing to the chemical
evolution of galaxies. We discuss the importance of radiation pressure on dust
in determining the galaxies large-scale properties, and consider the
possibility of the central black hole directly shaping its host galaxy through
AGN feedback.
