Mid-Midpoint

Geometry Level 5

$ABC$ is a triangle with circumcenter $O$ , obtuse angle $BAC$ and $AB < AC$ . $M$ and $N$ are the midpoints of $BC$ and $AO$ respectively. Let $D$ be the intersection of $MN$ with $AC$ . If $AD = \frac {1}{2} (AB+AC)$ , what is the measure (in degrees) of $\angle BAC$ ?