Incenter and midpoints! Boom!

Geometry Level 5

Given \(\triangle_{ABC}\). \(I\) is the incenter of \(\triangle_{ABC}\), \(D\);\(E\) are the mipoints of \(AC\);\(AB\),respectively. \(DI\) intersects \(AB\) at \(Q\) and \(EI\) intersects \(AC\) at \(P\).

We know that \(S_{ABC} = S_{APQ} \), find \(\angle BAC\) in degree.

Clarification: \(S_{ABC} \) and \(S_{APQ}\) denote the area, respectively, of the triangles \(ABC\) and \(APQ\).

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