I'm having trouble figuring out how to react to collision between two circles in a 2D environment. I've found the point of collision, the center position of the circles at the time of collision, and the velocities at the time of collision. I'm looking to apply some force to the point of collision to both circles based on their velocities. But for the life of me, I have no idea how to do this or even where to start. I'm guessing some of the things I need to take into account are Velocities Mass Point of collision relative to the center of the circles Whether the force being applied is a 'helping' force or an 'opposing' force ('helping' if the force and the velocity of the circle are in the same general direction, 'opposing' if they are in the opposite directions, which will probably need checked for both X and Y individually) Any help would be appreciated.

You're not applying forces, you're applying impulses (instantaneous changes in momentum: infinite forces over infinitesimal times).

There's a bunch of collision handling literature out there that I'm sure some helpful people will post in response. I'll just say that for this simple case, you just need the following equations:

[Total Energy before collision] = [Total Energy after collision]
[Total momentum before collision] = [Total momentum after collision] .

This is enough to solve for the final momenta -- or, equivalently, for the changes in momenta (impulses).