lineTo problem

I have been working on a drawing “game” in my spare time (which is limited). This is probably a common question, if so I appologize. By the way, I do not have the code here, it is on my other computer. Anyway, I was using the lineTo method and a timer listener to fire the addition of each new line segment, if that makes sense. The problem is that when you draw an arc quickly, it looks terrible. It draws straight lines. I tried adjusting the timer, which helps a bit but still not great. I looked at the curveTo but could not figure out a logical way to get the achor coordinates. I did some research online and found some that use addChild with bitmaps. Has anyone tackled this before? Any advice?

Thanks in advance.