HMMT 2012 U1

Guts
Answer

Square $A B C D$ has side length 2 , and $X$ is a point outside the square such that $A X=X B=\sqrt{2}$ . What is the length of the longest diagonal of pentagon $A X B C D$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\sqrt{10}

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