Problem

2024 Mock AMC 12 - Problem 20

Square $ABCD$ has side length $13$ and point $E$ is constructed such that $BE = 7$ and $DE = 17$ . If the sum of all possible values of $AE$ is $k$ , find $k^2$ .

$\textbf{(A) }50\qquad\textbf{(B) }98\qquad\textbf{(C) }288\qquad\textbf{(D) }338\qquad\textbf{(E) }578$

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Category: Mock AMC 12
Points: 4
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