Changing corner radius on a shape changes unrelated anchor point
MacOS Big Sur 11.6, Illustrator 25.4.1
(Older versions too, I specifically reinstalled Illustrator with preferences resetted to verify if the bug is still there on the newest version)
I have been having this issue randomly for a while, when rounding corners on some shapes, certain anchor points get displaced, often ruining symmetry. I have tried turning every kind of snapping off. It doesn't matter if the corner is changed from the panel or from the artboard. Doesn't matter if I have one corner selected on more, Illustrator sometimes decides to change a certain anchor point.
Before rounding the corners, I drew the shape by hand, and substracted out a small 4px circle close to the middle with the pathfinder, to avoid having duplicate anchor points.
Attached image of my result, last image is a close-up of the wonky anchor point.

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I see what is happening, and can explain why it happens...
Ai’s approach to round corners is a peculiar one...
It doesn’t know if a corner was rounded, it keeps no tags for these, but it can detect arcs — and when it sees one, it draws a widget, calculating the reformed curve while you drag it or change the value numerically.
For some reason Ai’s solution does not allow to make two arcs meet in ONE point. Try to round two adjacent corners of a square, then click the merged point and drag it — you’ll see it’s actually two points. A tiniest gap should exist for the algorithm to work, it seems (although I have no idea why).
In this case, the logo was built without native widgets, and the circular arcs B and D have don’t have the Tiniest Gap... but when you start editing a corner with a widget, Ai converts the path into the one that can be edited with the rules established. And if two arcs can’t share a point by the rules, for Ai it means it’s not two arcs then, but only one rounded corner for a curved path. It makes it a not exactly 90°, and it makes the point shift.
To see what I mean, try to click the widget in the center of D and drag it into zero.To workaround the problem, select the shifting point before rounding corners and press 'Cut path at selected anchor points' in Control (or use Scissors with Smart Guides enabled) — this would force Ai to keep it when making a new rounded corner. When finished, press Ctrl+J to close the path back.
Another method would be to use a free Round Any Corner script by Hiroyuki Sato (https://shanfan.github.io/Illustrator-Scripts-Archive/) or Dynamic Corners plugin by Astute Graphics (https://docs.astutegraphics.com/vectorscribe/dynamic-corners)
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LAW de Groot commented
Thanks Egor,
A file to reproduce the bug is attached.
Also note how the control vectors in the counter shape of the B change considerably.
I do not know how the big circles were created, not my design. -
Not seeing it happening, but this feels familiar...
Do you happen to still have the file? If not — can you reproduce it from scratch?
In any way — can you tell how the larger rounded corner was created? -
LAW de Groot commented
When I add a small round corner to the sharp corner on the left, by double-clicking on the bullseye and entering a number, the non-selected right point moves a bit to the left. Eeeks!
(v29.8.1 Win) -
Here is a file provided by https://x.com/onthehead with a very simple test file.
Confirm and upvote. -
Oh, interesting.
Can you share the file?