[tex]\overrightarrow{AC}.\overrightarrow{DM}=0<=>\overrightarrow{AC}.(\overrightarrow{AM}-\overrightarrow{AD})=0<=>\overrightarrow{AC}.\overrightarrow{AM}-\overrightarrow{AC}.\overrightarrow{AD}=0<=>AC.AM.cos\widehat{MAC}=AC.AD.cos\widehat{DAC}<=>AM=AD.tan\widehat{MAC}[/tex]