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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