A'H/AA' = A'H.BC/AA'.BC = 2S(HBC)/2S(ABC) = S(HBC)/S(ABC) (1)
Tương tự : B'H/BB' = S(HCA)/S(ABC) (2); C'H/CC' = S(HAB)/S(ABC) (3)
Cộng (1),(2),(3) vế theo vế:
A'H/AA'+B'H/BB'+C'H/CC' = S(HBC)/S(ABC) + S(HCA)/S(ABC) + S(HAB)/S(ABC)
= [S(HBC) + S(HCA) + S(HAB)]/S(ABC) = S(ABC)/S(ABC) = 1