圆C:x^2+y^2-2x-4y-20=0,
配方得(x-1)^2+(y-20^2=25,
圆心C(1,2),半径r=5,
直线l:(2m+1)x+(m+1)y-7m-4=0,变为
m(2x+y-7)+x+y-4=0,
它过直线2x+y-7=0与x+y-4=0的交点A(3,1),
当AC⊥l时直线l被圆C截得的弦长最短,
AC的斜率=-1/2,
∴l的斜率=-(2m+1)/(m+1)=2,
∴-2m-1=2m+2,-3=4m,m=-3/4,
l:(-1/2)x+(1/4)y+5/4=0,即2x-y-5=0,
点C到l的距离d=5/√5=√5,
弦长=2√(r^2-d^2)=2√20=4√5.