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Value of angle BAC - Iran NMO 1998 (Second Round) Problem2

Source:

October 4, 2010
geometryincentercircumcircletrigonometrygeometry proposed

Problem Statement

Let ABCABC be a triangle. II is the incenter of ΔABC\Delta ABC and DD is the meet point of AIAI and the circumcircle of ΔABC\Delta ABC. Let E,FE,F be on BD,CDBD,CD, respectively such that IE,IFIE,IF are perpendicular to BD,CDBD,CD, respectively. If IE+IF=AD2IE+IF=\frac{AD}{2}, find the value of ∠BAC\angle BAC.
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