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Triangle A B C with A B=13 ,B C=5, and A...

Triangle `A B C` with `A B=13 ,B C=5,` and `A C=12` slides on the coordinates axes with `A` and `B` on the positive `x`-axis and positive `y`-axis respectively. The locus of vertex `C` is a line `12 x-k y=0.` Then the value of `k` is_____________

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