Precise branching ratio measurements of the decays D-0 ->pi(-)pi(+)pi(0) and D-0 -> K-K+pi(0) relative to the D-0 -> K-pi(+)pi(0) decay

Using 232 fb(-1) of e(+)e(-) collision data recorded by the BABAR experiment, we measure the rates of three-body Cabibbo-suppressed decays of the D-0 meson relative to the Cabibbo-favored decay, D-0 -> K-pi(+)pi(0). We find: (B(D0 ->pi-pi+pi 0))/(B(D0 -> K-pi+pi 0))=(10.59 +/- 0.06 +/- 0.13)x10(-2) and (B(D0 -> K-K+pi 0))/(B(D0 -> K-pi+pi 0))=(2.37 +/- 0.03 +/- 0.04)x10(-2), where the errors are statistical and systematic, respectively. These measurements are significantly more precise than the current world average measurements.