Two Circles Both Of Radii 4 Have Exactly One Point In Common. If A Is A Point On One Circle And B Is A Point On The Other Circle, What Is The Maximum Possible Length For The Line Segment AB?

16

if both circles have a radii of 4 then they have a diameter of 8,
if the point which the circles have in common is exactly at the opposite side of the circle to the points A and B

then the line AB would consist of both diameters added together....