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I mainly use Illustrator for layouts, so it is so incredibily frustrating to not be able to figure out how to make this path (forgive me if the term is wrong), from overlapping circles and lines (how I would do it with pencil and paper). I want the exact curvature I need for this repeating radial pattern. In the image I'm posting, I am showing 2 of the shapes that I would be using in a radial repeat.
 
Select all these lines.
Use the shapebuilder tool
Hold down Alt and then click (or click and drag on the parts you want gone.
When only those are left that you want to keep, Join them with Object > Path > Join
If you want to keep the center of the construction, mark it with Guides first.
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Hello @Zaxx81,
Thanks for reaching out. Would you mind sharing more details about your workflow, including some samples / videos, so we can better assist you?
Looking forward to hearing from you.
Thanks,
Anubhav
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What I need is the overlapping lines and cicle sements that I traced in blue, and the rest would be discarded.
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Using the Pen tool, assisted by Smart Guides, is an easy way to draw what you marked in blue, isn't it?
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I can't get the Pen tool to give the slight curvature that the circle has been lines.
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I don't understand why you won't get it with the Pen tool.
What hampers?
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How would I get the precise curvature of the circle part with the Pen tool?
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What tool did you use for the blue lines? The Pen tool gives the most precision.
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Screenshot and then brush in Photoshop.
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The paths indicated in blue could be created accurately using Pathfinder operations on copies of the circles and radiating straight lines. Initially the paths would have sharp corners, but the corners could have radius curves applied to them using two or more different methods in Illustrator.
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Select all these lines.
Use the shapebuilder tool
Hold down Alt and then click (or click and drag on the parts you want gone.
When only those are left that you want to keep, Join them with Object > Path > Join
If you want to keep the center of the construction, mark it with Guides first.
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Thank you! I was able to get my pattern and then do Object > Repeat > Radial.
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Glad you could solve it!
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Similar circular patterns are around $75 with commercial license, so glad i could do it myself!
 
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Glad you could solve it!
Here is another idea: Draw this border straight horizontally (much easier)
drag it into the Brushes panel (Window > Brushes)
Make a pattern brush
If you feel the need to edit that later for whatever purpose: Object > Expand appearance
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Awesome, that completely elimiated the need to even use curves! How would I adjust the brush settings so the shared line between the patterns overlap? Just remove the right line?
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Got it! Just removed the right line from the patter using the Direct Select Tool
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That's probably the best method when you want to later outline the strokes and combine them, but there is also another method. All pattern brushes have an invisible rectangle in the background (if you don't create it, Illustrator will do so automatically). You can use that in your favour to adjust the distance between pattern elements.
You can just draw that invisible rectangle or edit the one Illustrator created (in this video: bruhes panel, layers panel, color panel) https://youtu.be/2FUgL9XobGI
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I can't for the life of me figure out how to make the new Pattern Brush (no fill, only strokes) change stroke color when I use it.
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Nevermind, Object > Expand Appearance.
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Finished my design! Thank you everyone for your assistance.