The technique I described earlier will work for this. You have to use a mask to hide the lines from the center. Try this, create the line like I described before, and then create a mask using a compound path. Draw a circle that extends far beyond the lines. Then draw another circle that the size you want to hide the portion of the line you want hidden. Make sure this circle is in front of the larger circle as that will effect how the compound path is structured. Take the center circle and copy and paste in front (Command C and Command F) then hide this circle (Command 3) I’ll explain why in a moment.
Now, select just the two circles you’ve created, go under object, and scroll down to compound path and MAKE. What this does is create an object with a hole in the middle. If you were to fill this object, you’d have something that would look like an O. Now, make sure this object is in FRONT of the lines, select the object and the lines and go under object, scroll down to Clipping mask, and MAKE.
This should create the lines you want. Now remember the circle you hid. Bring it back (Command Option 3) and apply a stroke to it. Make it slightly smaller and you should have the effect you