$$left( overrightarrow{AB},overrightarrow{AM}
ight)=left( overrightarrow{AC},overrightarrow{AM}
ight)Rightarrow cos left( overrightarrow{AB},overrightarrow{AM}
ight)=cos left( overrightarrow{AC},overrightarrow{AM}
ight)$$
$$Leftrightarrow frac{overrightarrow{AB}.overrightarrow{AM}}{AB.AM}=frac{overrightarrow{AC}.overrightarrow{AM}}{AC.AM}Leftrightarrow frac{overrightarrow{AB}.overrightarrow{AM}}{AB}=frac{overrightarrow{AC}.overrightarrow{AM}}{AC}$$ (*).