  We investigate the recent and current star formation activity of galaxies as
function of distance from the cluster center in a sample of 521 SDSS clusters
at z<0.1. We show that when the BCGs are excluded from the galaxy sample, there
is no evidence for mass segregation in the clusters, so that differences in
cluster and field populations cannot simply be attributed to different mass
functions. We find a marked star formation-radius relation in that almost all
galaxies in the cluster core are quiescent, i.e. have terminated star formation
a few Gyr ago. This star formation-radius relation is most pronounced for
low-mass galaxies and is very weak or absent beyond the virial radius. The
typical star formation rate of non-quiescent galaxies declines by approximately
a factor of two towards the cluster center. However, the fraction of galaxies
with young stellar populations indicating a recently completed starburst or a
truncation of star formation does not vary significantly with radius. The
fraction of star-forming galaxies which host a powerful optical AGN is also
independent of clustercentric radius, indicating that the link between star
formation and AGN in these galaxies operates independent of environment. The
fraction of red galaxies which host a weak optical AGN decreases, however,
towards the cluster center, with a similar timescale as the decline of star
forming galaxies. Our results favor a scenario in which star formation is
quenched slowly, on timescales similar to the cluster crossing time, and rule
out significant contributions from more violent processes at least beyond
cluster radii >0.1 R_200.
