I’m not certain that I understand what you are saying, so please bear with me.

You can find any number of topics on this and other discussion boards about how SketchUp’s geometry representation includes only finite straight edges and finite planar faces bounded by closed sequences of edges (“loops”). And about how SketchUp has no higher-order geometric objects such as real curves or curved surfaces that you can find in other parametric modeling applications. These facts are fundamental to how SketchUp was designed and how it works; adding real circles or things like NURBS would require a very deep rewrite of the entire thing, not just an easy extension or fix.

So, yes, there are shapes that SketchUp can only approximate and operations involving those shapes that it can’t perform exactly. It comes down to understanding what SketchUp can do within its approximation and toolset and adapting expectations to the best approximation available - which can usually be good enough for all practical purposes.

I assume by your talk about “quadrants” your goal is to create something akin to this:

If you look closely, you can see that those two cylinders actually touch along a side edge from one of the vertices of the end circle.

There are two things to realize in creating such a structure:

- Only the vertices of the circles lie on the mathematical abstract circle. There are no points on the rest of the abstract circle, so the SketchUp objects wouldn’t touch even if you could grab or snap there. So the only places you can make the cylinders “kiss” is along a face or edge.
- When you draw a SketchUp circle, the first click sets the center point and the second click sets the location of the first vertex of SketchUp’s polygon approximation. If that second click isn’t along an axis direction from the center, none of the circle’s vertices will be exactly on that axis (which is what I assume you mean by “quadrant”). When that’s the case indeed you can’t pick a vertex that is exactly on the quadrant because there is none. As you wrote, you can get closer by increasing the number of segments in the circle approximation, but you will never be exact and you will have made your model quite heavy.

For a lighter-weight model, you can address the problem in either of two ways. You can draw the original circle/cylinder carefully to make sure it is oriented the way you require, or you can use the rotate tool to reorient the circle/cylinder after the fact to bring it into alignment. Then if you move one circle by grabbing a vertex and moving to the snap at a vertex of the other, you will have them touching as closely as SketchUp can do: