then, I want to find the distance $L$ to a different point on this circle, measured by angle $\theta$ which goes clockwise, like this:
Is there any way I can calculate $L$ as a function of $\theta$ and $L$? I tried doing some trigonometry but was unsuccessful.
What about in the more general case where the initial point of $L_0$ is not perpendicular to the circle? For example, this: