Animating an end of a line along a path. (In After Effects)
Importing stuff from Illustrator to AE is still a pain. Overlord is a good plugin that makes it a bit easier - it can transfer shapes to and from Illustrator. Also this script helps with putting selected objects in Illustrator onto their own layer.

If you want to move the end of a line around, you could make a null that follows the path of a circle.


Make a circle shape in AE. Make sure its position and its Shape position are 0,0.
Convert the circle path to bezier. Keyframe the path of the circle at the start of your timeline. 
Copy this single keyframe.
Make a null at position 0,0 
Paste your keyframe data into the position data of your null. 
Make a New solid layer.
Add a Beam effect to it.
Make sure the beam's length is set to 100%.
Parent one end of the beam to your null layer.
Move the other end on your circle.