You can also just plug any circle or arc into a point parameter and it will automatically convert to the center-point.
(until its been Oiented and Projected)
Unfortunately I cant Project the Point that created the circle with PROJECT
From the center of the circle and the normal of its plane you can create a line with “SDL” component and then use “IsoVist Ray” to get the first intersection with your brep.
It’s best to provide a minimal example file so others can help without recreating your scenario via guesswork. But your screenshot it appears that you no longer have a circle after projecting to a curved brep. The intersection will be a non planar curve. I’d recommend that you transform your centerline/axis then intersect that with the brep to get the end of the axis.
Project the original center on the same shape, and the projected circle is not a circle