The length of the common chord of the circles
\[
x^2+y^2-8x-6y-11=0
\]
and
\[
x^2+y^2-6x+8y+9=0
\]
is
Show Hint
The common chord of two circles is their radical axis.
Its length is
\[
\boxed{2\sqrt{r^2-d^2}},
\]
where \(d\) is the perpendicular distance from the centre to the radical axis.