I know that this is a very simple question, but I am stuck at the very last part of this process and can't find the solution elsewhere (I figured I'd find it on this site, but I didn't see it).
I have an object that is colliding with a circle and I need it to deflect properly, like this:
I know the coordinates of the center of the circle and the object when it is on the circle's perimeter. I know the direction that the object is traveling on contact and can calculate the direction to the center (pointing inwards).
From similar questions, I know that the tangent line is perpendicular to the radius line I calculate. But, I'm not sure where to go after that. I need to calculate the new direction of the object in degrees, but my idea $\theta = \theta + 2(radiusline - \theta)$ , where $radiusline$ is the vector pointing towards the center, is inaccurate.
What is the proper formula for this deflection?