Animating an end of a line along a path. (In After Effects) So in the image below you see 4 "frames". This is how I see this animation playing in my head.(sorry for quality). Basicly, what I wanna do is to animate one end of a line sliding on the path of the circle. One end (let's call it B) will be moving on the circle, while the other end (A) will be stationary. 

So I kinda know how to change position of a point on a path(and thus animate it), but I don't know how to make it move along some defined trajectory (or path; in this case the circle's arc). 

Also, a quick small question: is it possible to import a file from Adobe Illustrator into After Effects such that AE recognises the shapes as paths(I mean the ones that are paths in Illustrator). When I do the import, AE thinks those are just images, you know, general objects, not paths. I wanna do some geometry animation, so It'd be helpful I that kind of import would actually work.
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.