Show that for a lincar triatomic molecule

$l_b=\frac{m_1{m}_2{R}_{12}^2+m_1{m}_3{R}_{13}^2+m_2{m}_3{R}_{23}^2}{m_1{m}_2+m_3}$

where the atoms are labeled $1,2$ and $3,$ and where $R_{ij}$ is the distance between atoms i and $j.$ Hint: use $(R_{13}-R_{12}-R_{23}{)}^2=0.$