Six, as shown in the figure, the lengths of the three sides of $\triangle A B C$ are $B C$ $=17, C A=18, A B=19$. Through any point $P$ inside $\triangle A B C$, perpendicular lines $P D, P E$, $P F$ are drawn to the three sides of $\triangle A B C$ (with $D, E, F$ being the feet of the perpendiculars), and $B D+C E$ $+A F=27$. Find: $B D+B F$.
Six、 $B D+B F=18$.

 переведено как:

Six、 $B D+B F=18$.

However, the correct English translation should be:

Six. $B D+B F=18$.

Note: The original text uses a full-width comma and the number "Six" followed by a full-width period, which is preserved in the translation. If the format is to be strictly followed, the translation should use the same style. If a more standard format is preferred, the translation provided is more appropriate.