So let's assume I have a point $P$ in $3d$ space $(x_0, y_0, z_0)$. And I have a circle $C$ that is centered at $(x_1, y_1, z_1)$ with a radius $r$. I need to find the distance from $P$ to the nearest point of $C$. I'm not totally sure how to define a circle in $3d$ space, so suggestions there would help too :D
I really have very little idea where to begin with this (and I only have a very basic understanding of how to do the same thing with a point and a line). I haven't taken a math class in a number of years, but this concept will help tremendously in some $3d$ programming I'm working on.