how to create a shape like this

Tristan,

As I (mis)understand it, you can create two circles of identical size or different sizes, then position them with an overlap that gives (at least) one crescent that ends at the bottom right, and then you can create a straight path across where you wish to cut it. You can let the Shape Builder Tool rid you of unwanted parts.

You can have a look here and/or here:

https://helpx.adobe.com/illustrator/using/creating-shapes-shape-builder-tool.html
https://helpx.adobe.com/illustrator/atv/cs5-tutorials/creating-complex-art-with-the-shape-builder-tool.html

You probably cannot make it part of a circle, but you could start with a copy of the circle, apply a width profile and removet the left and bottom anchor points.