# Prove that planes $AOA',BOB'$ and $COC'$ pass through the line $\frac{x}{l_1+l_2+l_3}=\frac{y}{m_1+m_2+m_3}=\frac{z}{n_1+n_2+n_3}$

$O$ is the origin and lines $OA,OB$ and $OC$ have direction cosines $l_1,m_1,n_1;l_2,m_2,n_2;l_3,m_3,n_3$ respectively.If lines $OA',OB'$ and $OC'$ bisect angles $BOC,COA$ and $AOB$,respectively,prove that planes $AOA',BOB'$ and $COC'$ pass through the line $\frac{x}{l_1+l_2+l_3}=\frac{y}{m_1+m_2+m_3}=\frac{z}{n_1+n_2+n_3}$ .