The length of the common chord of the circle x^2+y^2-6x-16=0 and x^2+y^2-8x-9=0 is

S1 has center (3,0) and radius 5
S2 has center (4,0) and radius 5
It’s easy to see it has a figure as follows

and we need to find AB.
as both the radii are same AB will be the perpendicular bisector of C1C2,
and we know that C1A =C2A = C1B = C2B = 5 and C1C2 = 1.
Now using very basic application of pythagoros theorm as