HMMT November 2016 H3

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The three points $A, B, C$ form a triangle. $A B=4, B C=5 A C=6$ . Let the angle bisector of $\angle A$ intersect side $B C$ at $D$ . Let the foot of the perpendicular from $B$ to the angle bisector of $\angle A$ be $E$ . Let the line through $E$ parallel to $A C$ meet $B C$ at $F$ . Compute $D F$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{2}

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