Resolve System of Circles out of Collision

Question

I have two circles: Circle $C$ and Circle $E$.

$E$ orbits $C$ with a fixed distance $||CE||$.

$E$ also penetrates the "wall" $AB$ by a certain length (red line in picture). What is the angle that I have to rotate $E$ around $C$ so that the penetration becomes zero?

Everything is known: the circle radii, $||CE||$, the penetration depth & normal, you name it.

This is the problem, this is the desired solution. (Can't post pictures here, don't have 10 rep yet.)

Thanks in advance!

-Thomas

Answer 1

Find the intersections of $E$’s orbit with a line parallel to $\overline{AB}$ that’s offset toward $C$ by a distance equal to the radius of $E$. Those intersections are the points on the orbit at which $E$ is tangent to $\overline{AB}$. I trust that you’ll be able to work out the angle from there.