@j.palmeL29YX wrote:
.... Instead ot the lenghten command you also can use the extend command. ....
In many cases those would work, but there are lots of configurations in which it becomes a little more complex, particularly if a vertex with a change in direction falls inside the Offset gap, like the red result here:

After Exploding the red resulting Polylines, for the Arc and the lower-left Line, Lengthen would need APParent-intersection Osnap, but that doesn't work, or Extend could be used, but only in Standard mode with its Edge option set to Extend. Or Fillet with zero radius.
In the green situation, the lower-leftward Line and the longer Arc happen to be able to intersect [Extend with the same settings, or Fillet], but if the white arc segment were of smaller-enough radius [grip-edit its midpoint leftward], that intersection wouldn't exist, and it would need to be Filleted with a non-zero radius like the upper right corner.
Etc., etc. I doubt a routine could be made to work under any geometric configuration, but if there are only limited possible relationships, maybe something could be worked out. But I agree, it may not be worth trying to automate -- lots and lots of these could be handled manually in less time than it would take to come up with a routine.
Kent Cooper, AIA