How can I make an image like this?
When I try doing this in Adobe Illustrator, it ends up like this. the final few circles overlap with the first few. How do I avoid this?
Let me suggest a solution with a slightly better workflow. Recognize that the same shape repeats several times so let us first make that one shape. So:
Rotate circle by 360/8° from a corner point (Alt+LMB click). (replace 8 with any amount of petals you want)
Image 1: Rotate one copy
Use shape builder or pathfinder to carve out the one shape.
Image 2: Make one petal with shapebulilder. (or use pathfinder)
Rotate object by 360/8° from corner, then hit ctrl+D repeatedly until you have a full circle.
Image 3: Replicate by repeating last transform
Alright alright, do it like this:
Step 2: Arrange the first circle on top of the others (Right click > Arrange > Bring to Front).
Step 3: Select the last circle and the first one, click on the shape builder.
Step 4: Click on the last circle, this will cut it.
Step 5: Arrange the first circle to the bottom of the others (Right click > Arrange > Send to Back.
Step 6: You see the last circle will have a cut, it's 2 pieces now.
Delete the small piece and there you have it.
I wanted to create a scatter brush using a flower with overlapping petals (think plumeria) and did not want to use the Shapebuilder; I didn't want to cut all of the petals, as I wanted to be able to edit and adjust them later. Moreover, I had an expanded gradient in the petals and Shapebuilder does not treat such objects kindly since the expanded gradient is, in reality, a collection of shapes. Instead. I selected the strokes on the last petal and the first one, duplicated them and moved them off of the rest of the work.
Then I used the Pathfinder's 'Minus Front' tool to cut the last petal's overlap into the first petal.
Then I replaced the first petal's stroke with the cut one.
I realize that this is not the most elegant workflow, nor is it applicable to all such situations but it is workable in cases like this where the Shapebuilder cannot be used and it does have the virtue of preserving all of the shapes intact except for the one trimmed stroke, which can be recreated if necessary. This leaves you free to adjust and modify the various components.