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Triangle \( A B C \) has side-lengths \( A B = 12 \) \( \mathrm { BC } = 24 \) and \( \mathrm { AC } = 18 . \) The line through the incenter of \( \Delta A B C \) parallel intersects \( A B \) at \( M \) and \( A C \) at \( N \) the perimeter of \( \Delta \mathrm { AMN } \) to \( \mathbf { B C } \) What is

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