Question 4
The interior bisector of $\angle B$ and the exterior bisector of $\angle C$ of triangle $ABC$ meet at $D$. Through $D$, a line parallel to $CB$ meets $AC$ at $L$ and $AB$ at $M$, as shown. If legs $LC$ and $MB$ of trapezoid $CLMB$ have lengths 5 and 7 respectively, find $LM$.
