11. The line $l:(2 m+1) x+(m+1) y-7 m-$ $4=0$ is intersected by the circle $C:(x-1)^{2}+(y-2)^{2}=25$ to form the shortest chord length of $\qquad$ .
$11.4 \sqrt{5}$
Line $l$ passes through point $D(3,1)$, with the center of the circle being $C(1,2)$. The shortest chord is perpendicular to $CD$, and $CD^{2}=5$.
The half-chord length of the circle is $2 \sqrt{5}$, so the chord length is $4 \sqrt{5}$.