OMM 2001 Problem 5

$ABC$ is a triangle with $AB < AC$ and $\angle A = 2 \angle C$ . $D$ is the point on $AC$ such that $CD = AB$ . Let L be the line through $B$ parallel to $AC$ . Let $L$ meet the external bisector of $\angle A$ at $M$ and the line through $C$ parallel to $AB$ at $N$ . Show that $MD = ND$ .