I want to write some code that will "merge" two circles into each other. Let me illustrate:

[![enter image description here][1]][1]

I want the red circle to move toward the blue circle, in order to have the exact same size and position as the blue circle after, say, $n$ steps. But, as you can see in the picture, the top-left corner has to cover a lot more distance than the bottom-right corner.

Any ideas on this?


  [1]: https://i.sstatic.net/QP7ugm.png