HMMT 2012 G3

Geometry
Answer

Let $A B C$ be a triangle with incenter $I$ . Let the circle centered at $B$ and passing through $I$ intersect side $A B$ at $D$ and let the circle centered at $C$ passing through $I$ intersect side $A C$ at $E$ . Suppose $D E$ is the perpendicular bisector of $A I$ . What are all possible measures of angle $B A C$ in degrees?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{540^{\circ}}{7}

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