Point of Contact Between Arc and Circle

[mjgarrin]

Hello,
I have an arc with an arc length = 46.88 mm and radius = 44 mm.
I have an intersecting arc with an arc length = 26.69 mm and radius = 43.4 mm.

A circle with radius = 24 mm fits between the two arcs.

How can I determine the contact points of the circle and the two arc lines?

 

[mfb]

Do you know the position and orientation of those arcs? Do you know (or can you calculate) where their corresponding circle centers are?

You can determine the central point of the 24mm-circle as a function of the contact points, and see if you can set both points equal.