a) Ta có: $ΔABH \sim ΔCAH \, (g.g)$
$\Rightarrow \dfrac{AB}{AC} = \dfrac{AH}{CH}$
$\Rightarrow \left( \dfrac{AB}{AC}\right)^2 = \left( \dfrac{AH}{CH}\right)^2 = \dfrac{BH.CH}{CH^2} = \dfrac{BH}{CH}$
$\Rightarrow \dfrac{AB^2}{AC^2} = \dfrac{\left(\dfrac{AB.HD}{AH}\right)}{\left(\dfrac{AC.HE}{AH}\right)}$
$\Rightarrow \dfrac{AB^2}{AC^2} = \dfrac{AB.HD}{AC.HE}$
$\Rightarrow \dfrac{AB}{AC} = \dfrac{HD}{HE}$
b) Ta có: $\dfrac{AB^2}{AC^2} = \dfrac{BH}{CH}$ (câu a)
$\Rightarrow \dfrac{AB^4}{AC^4} = \left(\dfrac{BH}{CH}\right)^2 = \dfrac{BD.AB}{EC.AC}$
$\Rightarrow \dfrac{AB^3}{AC^3} = \dfrac{BD}{EC}$
