Check intersection of Segment_2 from Gmpq kernel with a Circle in CGAL

Question

Edit2: I have redefined my entire setup as the following:

typedef CGAL::Exact_circular_kernel_2 CircK;
typedef CGAL::Point_2<CircK> Point_2;
typedef CGAL::Segment_2<CircK> Segment_2;
typedef CGAL::Circle_2<CircK> Circle_2;

I still can't seem to find the proper function to do the intersection however... CGAL's examples mostly involve Circle_2 and Line_2 or just two circles.