We present a study of the optical brightness profiles of early type galaxies, using a number of samples of radio galaxies and optically selected elliptical galaxies. For the radio galaxy samples--B2 of Fanaroff-Riley type I and 3C of Fanaroff-Riley type II-- we determined a number of parameters that describe a Nuker-law profile, which were compared with those already known for the optically selected objects. We find that radio active galaxies are always of the core type (i.e. an inner Nuker law slope gamma < 0.3). However, there are core-type galaxies which harbor no significant radio source and which are indistinguishable from the radio active galaxies. We do not find any radio detected galaxy with a power law profile (gamma > 0.5). This difference is not due to any effect with absolute magnitude, since in a region of overlap in magnitude the dichotomy between radio active and radio quiescent galaxies remains. We speculate that core-type objects represent the galaxies that have been, are, or may become, radio active at some stage in their lives; active and non-active core-type galaxies are therefore identical in all respects except their eventual radio-activity: on HST scales we do not find any relationship between boxiness and radio-activity. There is a fundamental plane, defined by the parameters of the core (break radius r_b and break brightness mu_b), which is seen in the strong correlation between r_b and mu_b. The break radius is also linearly proportional to the optical Luminosity in the $I$ band. Moreover, for the few galaxies with an independently measured black hole mass, the break radius turns out to be tightly correlated with M_{BH}. The black hole mass correlates even better with the combination of fundamental plane parameters r_b and mu_b, which represents the central velocity dispersion.
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