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.
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