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}