# The Feet Of Perpendiculars From The Internal Bisector

Geometry Level 3

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In acute triangle $$\triangle ABC,$$ the internal angle bisector of $$\angle BAC$$ meets $$BC$$ at $$D.$$ $$E, F$$ are the feet of perpendiculars from $$D$$ on $$AC, AB$$ respectively. Let $$O$$ be the circumcenter of $$\triangle AEF.$$ Given that $$\angle BAC = 60^{\circ},$$ find $$\angle BAO$$ in degrees.

Details and assumptions

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