The lines of the circle and line interact perfectly but when I expand and divide it looks like the stroke setting throws it off and the shapes don't meet perfectly?
I am zoomed in a lot so not sure if this is the best I can get it?
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You should draw the lines so that they really snap in the same points:
The red line is drawn by having smart guides ON. They indicated "crossing" at the line ends. Often the scene is tighter and smart guides give too many indications. Then I have inserted new anchor points to the crossings and kept Snap to points ON.
If the line must be longer it can be stretched by holding the Shift key at the same time. That keeps the direction. Also the midpoint stays if you hold Alt+Shift when you stretch the line.
Expand sounds bad. The lines become filled areas. Just that can be your problem.
When the line is stretched one can fill the areas with the Shape Builder:
The borders of the areas are exactly in the middle of the curves.
The fill color is changed between the fills.
Learn the Shape Builder tool from the User's Guide. It's one of those Illustrator's extraordinaries that the makers of low cost graphics programs haven't succeeded to rival, no matter they have had more than a decade time to do it.
Deleting the remnants, removing the strokes and zooming in to the maximum do not reveal any errors
ADD: Checked questioner's version. 6400% (no more available here) zoom in doesn't show any error in my legacy Windows system.
But the corner node in the 3rd version where 3 colored shapes meet looked somehow thick. I selected the nodes with the direct selection tool and aligned them horizontally and vertically. The node became as thin as a single node.
I repeated questioner's drawing steps (=used Pathfinder Division instead of the Shape Builder). Scaling the image to 1000% and watching with 6400% zoom in revealed some error:
Pathfinder (see its options menu) has precision setting. But reducing the allowed error didn't make it better. So, the problem stays unexplained. Maybe the limit of the used math has been met.
Try as a workaround to select the nodes of the corner with the direct selection tool and align horizontally and vertivally.
Shape builder made it still OK, no visible error after scaling.
This is more of a guess than anything....
After the divide operation, with everything still stroked, if you are seeing something such as this...
It's due to the angle created at the anchor points. There are two possible solutions here...
Limitfield on the Stroke Panel) to a value that doesn't create a sharp point
The larger mystery to me is... if you remove the strokes and then apply fills, this should never be an issue. That little piece is only there because of the strokes.
You seem to be getting that "spare" shape because you are doing something between the divide and subsequent filled shapes. What that is, I don't know. I can only guess that you may be possibly expanding the strokes at some point? Or using something like Live Paint rather than merely adding fills?