Creating an arc with the same gradient as the arc of an inner ring

[d__]

Hi,

I'm trying to create a swirl type shape which consists of two arcs (lines with uniform gradient change) which are joined together at one point, and then by a line at the other two.
However the Upper arc, needs to have the same gradient as inside of a ring I created earlier. I'm having trouble creating the swirls, and I was wondering if there were a way of doing, this or even just general advice on the subject at hand.

I understand that what i've asked sounds incredibly complex so I've attached a few images to help illustrate my problem.
The shape I want to create is shaded in red, and uses a an arc I drew using the arc tool, and hopefully the inner arc of the purple ring.

Thank you for any help or advice,
-Dan