HMMT 2012 S1

Team 2
Answer

Triangle $A B C$ has $A B=5, B C=3 \sqrt{2}$ , and $A C=1$ . If the altitude from $B$ to $A C$ and the angle bisector of angle $A$ intersect at at $D$ , what is $B D$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{5}{3}

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