# 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 $\angle BAC$?

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