c)Gọi $M$ giao điểm của $BC,OA$$\triangle AMK\sim \triangle AHO\Rightarrow AK.AH=AM.OA$
$\triangle ABO\sim \triangle AMB\Rightarrow AB^2=OA.AM$
$\Rightarrow AK.AH=AB^2$
$\triangle ABD\sim \triangle AEB\Rightarrow AB^2=AE.AD$
$\Rightarrow AE.AD=AK.AH$
Xét $2.AK.AH-AD.AK=AK.(2AH-AD)$
$=AK.(AH+AH-AD)$
$=AK.(AH+DH)=AK.(AH+HE)=AK.AE$ vì ( $DH=HE)$
$\Rightarrow 2AK.AH=AD.AK+AK.AE$
$\Rightarrow 2.AK.AH=AK.(AD+AE)$
$\Rightarrow \frac{2}{AK}=\frac{1}{AD}+\frac{1}{AE}$