So the question goes something like this: Now I've already found the solution to the problem, so I don't need any assistance there, and why I'm not posting this in homework help. What I'm having trouble with is visualizing the situation at some instant right before the cat catches the mouse. It seems to me that if I look at some ##d\theta##, when the mouse and cat are some ##dx## distance apart, they would need to run parallel to one another at the same velocity to maintain the co-linear requirement (basically the limiting case where the distance approaches zero?). So it would seem like the cat and mouse would never actually meet. I'm thinking this since if it stepped off the current track it would need to violate one of the two conditions, or end up some ##dx## behind the mouse. I haven't been able to reconcile the above to my satisfaction. My first thought was maybe it's because the curves are only approximately straight lines at some small angle, and the components of the velocities are only approximately equal at some ##dx##, such that the cat would still have a small bit of velocity left over to approach the mouse and still remain co-linear with the center of the circle until they actually meet- as the cats radius would still be some ##dx## smaller than the mouses. I can't think of a good way to see this though. Is there some concept I'm missing here? Does this even make sense to anyone else?