\(\eqalign{
& MN\,\,la\,\,duong\,\,TB\,\,cua\,\,\Delta ABH \cr
& \Rightarrow MN//AB\,\,va\,\,MN = {1 \over 2}AB \cr
& \Rightarrow MN//CK\,\,va\,\,MN = CK \cr
& \Rightarrow MNCK\,\,la\,\,hinh\,\,binh\,\,hanh \cr
& \Rightarrow MK//CN\,\,\left( 1 \right) \cr
& Ta\,\,co\,\,MN//CK.\,\,Ma\,\,CK \bot BC \cr
& \Rightarrow MN \bot BC \cr
& Xet\,\,\Delta BCM\,\,co: \cr
& MN \bot BC \cr
& BH \bot MC \cr
& MN \cap BH = N \cr
& \Rightarrow N\,\,la\,\,truc\,\,tam\,\,cua\,\,\Delta BCM \cr
& \Rightarrow CN \bot BM\,\,\left( 2 \right) \cr
& Tu\,\,\left( 1 \right)\,\,va\,\,\left( 2 \right) \Rightarrow MN \bot BM\,\,\left( {dpcm} \right) \cr} \)