Bulgaria National Olympiad Problem 2

Geometry Level 5

Let \(ABC\) be an equilateral triangle with an area \(7\) and let \(M,N\) be points on sides \(AB,AC,\) respectively, such that \(AN=BM\) and \( BM < MA \). Denote by \(O\) the intersection of \(BN\) and \(CM\). Assume that triangle \(BOC\) has area \(2\).

Find \(\angle AOB\) in degrees.

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