- Rotate each circle 45° (causing them to have an overlapping anchor point)
- Use the Direct Selection Tool (White arrow) to click anchors and delete them, leaving appropriate segments.
- Select the middle 2 anchor points and join them (
Object > Path > Join)
Rather than rotating the circles, you could also use
Object > Path > Add Anchors to create additional anchor points for smaller segments. New anchor points are added halfway between existing anchor points. In this case, you may not need to rotate the circles. They will inherently gain an overlapping anchor point.
Source : Link , Question Author : JamalDols , Answer Author : Scott