Q:

Illustrator shape builder tool precision error

I was trying to make a shape like below.
(All the circles are perfect circles and they encounter each other at one point only.)
I made the shape in Illustrator like this.  

I got 2 problems with this.
1. The shadings aren't matching the blue borders.
2. When I use the shape builder tool the result does not follow the blue boarders. (The temporary gray shading made by the shape builder tool to show the new border does not follow the blue borders. Image below)

I want this to be smooth and be mathematically perfect circles meeting at one point.
I'm currently using Adobe Illustrator CC 23.0.

A:

Maybe the shape builder is what's causing your issues. Here I created three ovals using the eclipse tool:

Now, if you press control/cmd + Y and then select your shapes with the direct selection arrow, you can go into outline mode and see where your anchor points are:

If all your ovals are not meeting at the bottom, I would make sure you do the following:
- View > Snap to Pixel
- Select all of your ovals with the direct selection tool
- While all of your ovals are selected, make the largest one the Key Object by clicking on it again (you'll know this because the Key Object is outlined in bold):
[
- Use the align palette, and notice how it will align to your key object, to make all of the ovals meet Vertical Align Bottom and Horizontal Align Center
Now they should all meet perfectly at the bottom anchor point.
To note: make sure your shapes are strokes, and not Expanded strokes. Also, it may be helpful to work with fill shapes rather than strokes as the strokes may cause a visual confusion when zooming in like we are here.
Good luck!

