Abstract: Precision measurements in atomic systems serve as powerful probes for studying nuclear structure as well as for testing for possible violation of the discrete symmetries. In the first part of this talk, our measurements of the nuclear charge radii of helium-8 and helium-6 will be discussed. The charge radius measurements of these short-lived neutron-rich isotopes serve to test the most precise nuclear models. In the second half of the presentation, our work towards a search for the permanent electric dipole moment (EDM) of radium-225 will be reviewed. The existence of a non-zero EDM signifies the violation of parity (P) and time-reversal (T) symmetry. Radium-225 is believed to be particularly sensitive to T- and P-odd interactions because of its unique nuclear structure.