kẻ đường cao AH có: \(\frac{OA'}{AA'}=\frac{S_{BOC}}{S_{ABC}}\), ta có:
\(\frac{OB'}{BB'}=\frac{S_{AOC}}{S_{ABC}}\)
\(\frac{OC'}{CC'}=\frac{S_{AOB}}{S_{ABC}}\)
\(\Rightarrow\frac{OA'}{AA'}+\frac{OB'}{BB'}+\frac{OC'}{CC'}=\frac{S_{BOC}+S_{AOC}+S_{AOB}}{S_{ABC}}=\frac{S_{ABC}}{S_{ABC}}=1\) (đpcm)
Nguồn: HiệU NguyễN