How do I find (easily) the center of a circle in Inkscape?

if you never moved the rotation center, click on the circle and click again on it, and the rotation center is at the geometric center.

In a true circle, the rotation center is also the true center. So just clicking twice with the Selection tool will reveal the rotation center. (It's a crosshair or plus sign.)

However, I suspect you want to put a dot or a path or something there. And it may depend on exactly what you need to do, once you find the center.

Snapping can be set up to snap things to both the rotation center and true center (they aren't always the same). And you can also set up snapping, to snap to the center of the bounding box (which isn't necessarily the same as either the rotation center or true center....at least, that's my understanding).

If you can give me some more info about what you need to do after you find the center, I can suggest how it might be done :-)

Sorry Mc, you posted while I was typing.