\(\eqalign{ & {S_{HBC}} + {S_{HAC}} + {S_{HAB}} = {S_{ABC}} \cr & \Rightarrow {{{S_{HBC}}} \over {{S_{ABC}}}} + {{{S_{HABC}}} \over {{S_{ABC}}}} + {{{S_{HAB}}} \over {{S_{ABC}}}} = 1 \cr} \)
\(\Rightarrow\eqalign{{HA'.BC} \over {AA'.BC}} +\eqalign {{HB'.AC} \over {BB'.AC}} \) \(+ \eqalign{{HC'.AB} \over {CC'.AB}} = 1\)
\( \Rightarrow \eqalign{{HA'} \over {AA'}} + \eqalign{{HB'} \over {BB'}} +\eqalign{{HC'} \over {CC'}} = 1\)
