Question

[nguyen thi thu Thuy]

cho tam giac ABC dg cao AD,BE,CF cat nhau tai H .Gia tri bt \(\frac{HD}{AD}+\frac{HE}{BE}+\frac{HF}{BF}\) 

Answer 1

[Huy Anh Lê]

\(\frac{H\text{D}}{A\text{D}}+\frac{HE}{EB}+\frac{HF}{CF}=\frac{H\text{D}.BC}{A\text{D}.BC}+\frac{HE.AC}{EB.AC}+\frac{HF.AB}{CF.AB}=\frac{2S_{BHC}}{2\text{S}_{ABC}}+\frac{2\text{S}_{AHC}}{2\text{S}_{ABC}}+\frac{2\text{S}_{ABH}}{2\text{S}_{ABC}}\)=\(\frac{2S_{HBC}+2S_{HAC}+2S_{HAB}}{2S_{ABC}}\)=\(\frac{2\text{S}_{ABC}}{2\text{S}_{ABC}}\)=1