  In this paper, we describe the XENON100 data analyses used to assess the
target-intrinsic background sources radon ($^{222}$Rn), thoron ($^{220}$Rn) and
krypton ($^{85}$Kr). We detail the event selections of high-energy alpha
particles and decay-specific delayed coincidences. We derive distributions of
the individual radionuclides inside the detector and quantify their abundances
during the main three science runs of the experiment over a period of $\sim$ 4
years, from January 2010 to January 2014. We compare our results to external
measurements of radon emanation and krypton concentrations where we find good
agreement. We report an observed reduction in concentrations of radon daughters
that we attribute to the plating-out of charged ions on the negatively biased
cathode.
