$$\eqalign{
& A{H^3} = BC.BE.CF \cr
& \Rightarrow A{H^3}.AH = AH.BC.BE.CF \cr
& \Rightarrow A{H^4} = AB.AC.BE.CF \cr
& \Rightarrow A{H^4} = AB.BE.AC.CF \cr
& \Rightarrow A{H^4} = B{H^2}.C{H^2} \cr
& \Rightarrow A{H^2} = BH.CH\,\,\left( {luon\,\,dung} \right) \cr
& Vay\,\,ta\,\,co\,\,dpcm \cr} $$