HMMT 2006 G8

Geometry
Answer

Triangle $A B C$ has a right angle at $B$ . Point $D$ lies on side $B C$ such that $3 \angle B A D=$ $\angle B A C$ . Given $A C=2$ and $C D=1$ , compute $B D$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3}{8}

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