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Square ABCD has side length 1 unit. Points E and F are on sides AB and CB, respectively, with AE = CF. When the square is folded along the lines DE and DF, sides AD and CD coincide and lie on diagonal BD. The length of segment AE can be expressed in the form \(\sqrt k-m\) units. What is the integer value of k + m?

 Jan 13, 2024

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