Say we have two circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$, respectively. Let their centers be $d$ units apart. There are 4 bitangents, two outer and two inner.
Examine the intersection of an inner bitangent with an outer one, near $C_1$. I'm looking for the value of the angle in the quadrant that contains $C_2$ in terms of $r_1$, $r_2$, and $d$.
Anyone have a reference (or a solution) for this? I'm sure it's been looked at before, but I don't know where to look.