Ta có:
$\dfrac{HA'}{AA'}+\dfrac{HB'}{BB'} +\dfrac{HC'}{CC'}$
$= \dfrac{\dfrac12HA'.BC}{\dfrac12AA'.BC}+\dfrac{\dfrac12HB'.AC}{\dfrac12BB'.AC} +\dfrac{\dfrac12HC'.AB}{\dfrac12CC'.AB}$
$=\dfrac{S_{BHC}}{S_{ABC}}+ \dfrac{S_{AHC}}{S_{ABC}}+\dfrac{S_{AHB}}{S_{ABC}}$
$=\dfrac{S_{BHC} + S_{AHC} + S_{AHB}}{S_{ABC}}$
$=\dfrac{S_{ABC}}{S_{ABC}}=1$