Given two circles c1 and c2 with velocity vectors v1 and v2, it would seem as though what you need to do really is calculate intersection points between two pairs of lines.  

 

 

I don't think that solves anything. The two circles might get to the intersection region at different times, and then they won't collide.

1AM me says my solution makes perfect sense - 7AM me says 1AM me should have went to bed.  

Given two circles c1 and c2 with velocity vectors v1 and v2, it would seem as though what you need to do really is calculate intersection points between two pairs of lines.  

 

 

I don't think that solves anything. The two circles might get to the intersection region at different times, and then they won't collide.

1AM me says my solution makes perfect sense - 7AM me says 1AM me should have went to bed.   I don't know what the heck I was thinking.   =P