c) $∆AEH\sim ∆AHB$
$\Rightarrow \dfrac{AE}{AH} = \dfrac{AH}{AB}$
$\Rightarrow AH^2 = AE.AB$
$∆AFH\sim ∆AHC$
$\Rightarrow \dfrac{AF}{AH} = \dfrac{AH}{AC}$
$\Rightarrow AH^2 = AF.AC$
Do đó $AE.AB = AF.AC$
d) $∆BEH\sim ∆BHA$
$\Rightarrow BH^2 = BE.BA \, (1)$
$∆CEH\sim ∆CHA$
$\Rightarrow CH^2 = CE.CA \, (2)$
$∆BHA\sim ∆AHC$
$\Rightarrow AH^2 = BH.CH \, (3)$
$(1)(2)(3) \Rightarrow BE.BA.CE.CA = BH^2.CH^2 = AH^4$
