RESOLVED - Segment Count Calculation for concentric circles?

I am needing to cut a chuck out of a donut shaped object for use in our manufacturing production as a mold filler.
I am struggling with being able to cleanly chop the donut to the final width and I know it has something to do with the segment count of the rings.
I was playing around and figured there has to be some sort of calculation available for it based upon the radius and desired width and possible the layer height in printing.

Attached is an example of one of the “donuts” I am needing to chop up. The end goal looks like these:

The goal is to have the section parallel, unlike that red 6 in the pic.
It seems like my lines always end up cockeyed or off at an angle, based upon where the circle segments end.

Does anyone know a way to cleanly plane off a section of a donut shaped item?

I am attaching a SKP file for an example.
Thank you,
SegmentDemo.skp (1.3 MB)

For more info on what I mean by segment count calculation, think of this:
Take 2 circles, one with a 100mm radius, the other with a 200mm radius and stack them, If they both have 24 segments, then the segment length of the 200mm circle will be longer, so if you need to slice out a section, it will be pie shaped instead of parallel.
I am wondering of there is a calculation to see how many segments are needed to make the other circle have the segment “ends” line up.

What makes my situation more difficult is that the “donut” is tapered, so the second layer of circles are a different size, so the segment counts would need to correlate with all 4 circles.

That is why I am wondering if there is a simpler “cut across a plane” function that I have not seen yet.

I saw this post: Cut a cylinder in two
But I am not sure if this is possible.

As in @Gully_Foyle’s example, cutting planes are what you need.

SegmentDemo_Cutting Plane Example.skp (319.6 KB)

You might try this approach using the arc tool to create the same number of segments between the parallel lines. Something like this, maybe:

[added] In the video, I push the rectangle straight through the block … I should have used the same technique to create the hole using whole segments as well:

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I never thought to try using just the arc tool, this would have saved me so much time in the past.
I will try it and let you know how it goes. The shrinking of the top to get the taper is going to be fun. but I think I can use the ruler tool to mark how far I need to move things before actually moving it.

Thank you!
The Arc Tool with a rectangle worked like a charm. The revisioning process was also much faster as this style of initial creation allowed me to resize the taper little by little instead of having to start over from scratch like the way I was doing it before.

This one only took me 8 tries to get a perfect fit versus the 26 it took me to get one of the other sizes completed, plus it took much less time.

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