2. Given $\triangle A B C$ with side lengths $a=17, b=18, c$ $=19$, a point $O$ inside $\triangle A B C$ is drawn perpendiculars to the three sides of $\triangle A B C$, intersecting at points $D$, $E$, and $F$, such that $B D+C E+A F=27$. Then $B D+B F$ $=$ $\qquad$