  We report a method for the precision measurement of the oscillator strengths
and the branching ratios of the decay channels of the $6d7p$ $^3F_2$ state in
$^{226}$Ra. This method exploits a set of metastable states present in Ra,
allowing a measurement of the oscillator strengths that does not require
knowledge of the number of atoms in the atomic beam. We measure the oscillator
strengths and the branching ratios for decays to the $7s6d$ $^3D_1$, $7s6d$
$^3D_2$, and $7s6d$ $^1D_2$ states and constrain the branching ratio to the
$7s6d$ $^3D_3$ state to be less than 0.4$\%$ (68$\%$ confidence limit). The
lifetime of the $^3F_2$ state is determined to be $15 \pm 4$ ns.
