Angle bisectors

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 $M$ . If the measures of legs $LC$ and $MB$ of trapezoid $CLMB$ are $5$ and $7$ , respectively, find the measure of base $LM$ .