Illustrator: Extra anchor points after divide 2 objects - unnecessary extra objects

Question

Can anybody help me with the following problem, please?

When I made a round object and put another round object on it they were perfectly fit together, but after I used Divide tool it gave extra anchor points to them and created unneccessary paths. I tried the tool on more types of objects, but I only have problems when it includes round objects.

So far I have not faced this kind of problem and I don't know how to fix it.

To let you know the problem better, I am attaching some pictures.

This is how my object looks like before and after using Divide tool:

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EDIT after answer:

Thank you for your help.

Maybe I do something wrong, but when I put the two objects on each other they look perfectly aligned even with 3600% zoom in. The two objects are the same as I created the green one with Minus front from the red one.

And when I put a 3rd object on them which completely overlaps them, de Divide tool still creates extras.

So this is how my shapes looked before using the tool:

This is how it looks after:

And when I put the 3rd object on them, this is what I got(before and after):

When I make the upper object bigger it works correctly, but my problem is that I need both (in this case green and red), just need to cut out something from them (blue).

Answer 1

Those points appear because Bézier curves are approximated and when performing boolean operations (unify, trim) the overlapping segments don't overlap exactly.

This problem will appear even with straight lines, where extra anchor points may appear when unifying shapes.

The solution is simple. Make sure the object that is trimming the another is bigger:

The above figure shows the edited object (red) that will trim correctly the black object. Simply use the Direct Selection tool and move the anchor points away so that the edges of the object to not touch. If you need the intersection of the objects that will work correctly as well.