That is possible with the API today, with a little work. The information is there; it's just that code must be written to dig it out and make sense of it. Here's a variation of the original problem, where three circles have been drawn.

This results in the four profiles shown below.

Circle 1 defines A, B, and C
Circle 2 defines A, B, and C
Circle 3 defines A and D.
To get this using a program the following is available in the API. The Profile object supports the profileLoops property, which returns a ProfileLoops object. A loop defines a connected set of geometry that defines the shape of the profile Profiles B, C, and D all have one loop. Profile A has two loops, one that defines its outer loop and another that defines the inner loops for the hole made by circle 3.
A profile loop specifies if it defines the outside or the inside of the profile. For example, with Profile A, one of the loops will be the outer loop, and from the loop, you can get the profile curves that make up the loop. The geometry of the two ProfileCurve objects of the outer loop will be two arcs that will be returned as Arc3D objects. Also, from the ProfileCurve object, you can get the sketch geometry that resulted in its creation. In this case, one of the profile curves will return circle 1 and the other will return circle 2. The other loop is an inner loop and has a single profile curve which is defined by circle 3.
Using that information, it's possible to write a function that will determine:
Circle 1 contributes to profiles A, B, and C
Circle 2 contributes to profiles A, B, and C
Circle 3 contributes to profiles A and D.
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Brian EkinsInventor and Fusion 360 API Expert
Website/Blog:
https://EkinsSolutions.com