  Locating the exact point of origin of the core radiation in active galactic
nuclei (AGN) would represent important progress in our understanding of
physical processes in the central engine of these objects. However, due to our
inability to resolve the region containing both the central compact object and
the jet base, this has so far been difficult. Here, using an analysis in which
the lack of resolution does not play a significant role, we demonstrate that it
may be impossible even in most radio loud sources for more than a small
percentage of the core radiation at radio wavelengths to come from the jet
base. We find for 3C279 that $\sim85$ percent of the core flux at 15 GHz must
come from a separate, reasonably stable, region that is not part of the jet
base, and that then likely radiates at least quasi-isotropically and is
centered on the black hole. The long-term stability of this component also
suggests that it may originate in a region that extends over many Schwarzschild
radii.
