# 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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