17. In triangle $A B C, \angle B A C$ is $120^{\circ}$. The length of $A B$ is 123 . The point $M$ is the midpoint of side $B C$. The line segments $A B$ and $A M$ are perpendicular. What is the length of side $A C$ ?
SolUtion
246

Extend the line $B A$. Draw a line through $C$, parallel to $M A$, meeting the extended line $B A$ at point $N$. By the intercept theorem, $B A=A N=123$, because $B M=M C$. In triangle $N A C, \cos 60=\frac{1}{2}=\frac{123}{A C}$. Therefore, $A C=246$.