The Feet Of Perpendiculars From The Internal Bisector

Geometry Level 3

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

Details and assumptions

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