HMMT 2007 G9

Geometry
Answer

$\triangle A B C$ is right angled at $A . D$ is a point on $A B$ such that $C D=1 . A E$ is the altitude from $A$ to $B C$ . If $B D=B E=1$ , what is the length of $A D$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\sqrt[3]{2}-1

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