Mid-Midpoint

Geometry Level 5

ABCABC is a triangle with circumcenter OO, obtuse angle BAC BAC and AB<ACAB < AC. MM and NN are the midpoints of BCBC and AOAO respectively. Let DD be the intersection of MNMN with ACAC. If AD=12(AB+AC)AD = \frac {1}{2} (AB+AC) , what is the measure (in degrees) of BAC \angle BAC?

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