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I divided the circle below using the following steps:

  1. made a perfect circle
  2. created two lines at 75 and 105° rotation
  3. used the pathfinder divide tool to separate the circle.

enter image description here

I want to know (how to calculate) the positions I would have to move each part of the circle to create an 80px gap. I would like to move each of them by an equal distance to create the 80px gap, as in the image. How can I find the new positions?

  • Each of the intersections is at an angle of 15° from vertical. At 45°, you'd move it as far down as sideways, so 45° = 100% and 15° is then 33.3%. Shouldn't this just be moving the side bits 80px to the side and then 1/3 of 80px (26.6px) downwards? (Disclaimer: IANAM!) Edit: Actually, easier way. Just rotate the whole thing -15°, move side bit 80px to the side, rotate whole thing 30°, move other side 80px to the side, and rotate whole thing -15° to get back to starting point. – Janus Bahs Jacquet Aug 16 '17 at 21:56
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Use the Offset Path feature (Object → Path → Offset Path...) on both line segments.

If those segments are already part of a larger path then just select the segments you need with the Direct Selection tool, then copy paste them... Run the Offset Path on both...

enter image description here

Then delete the parts you don't need...

enter image description here

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