Need help in checking type of edge/curve - cgal

Question

I have created a sample example for the intersection of two circles.
In this example I am able to get the bound faces and the source and target points.
I have manually plotted the source and target points. Refer snapshot for the same two intersecting circles:
I want to find out whether the edges between the source and target points is a line segment, arc or a circle.
I tried to find this in the 2D arrangement documentation but couldn't find it.
Below is the code snippet :
#include <CGAL/Cartesian.h>
#include <CGAL/Exact_rational.h>
#include <CGAL/Arr_circle_segment_traits_2.h>
#include <CGAL/Arrangement_2.h>
typedef CGAL::Cartesian<CGAL::Exact_rational> Kernel;
typedef Kernel::Circle_2 Circle_2;
typedef CGAL::Arr_circle_segment_traits_2<Kernel> Traits_2;
typedef Traits_2::CoordNT CoordNT;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::Curve_2 Curve_2;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
int main()
{
// Create a circle centered at (0,0) with radius 8.
Kernel::Point_2 c1 = Kernel::Point_2(0, 0);
CGAL::Exact_rational sqr_r1 = CGAL::Exact_rational(64); // = 8*^2
Circle_2 circ1 = Circle_2(c1, sqr_r1, CGAL::CLOCKWISE);
Curve_2 cv1 = Curve_2(circ1);
// Create a circle centered at (10,0) with radius 8.
Kernel::Point_2 c2 = Kernel::Point_2(10, 0);
CGAL::Exact_rational sqr_r2 = CGAL::Exact_rational(64); // = 8*^2
Circle_2 circ2 = Circle_2(c2, sqr_r2, CGAL::CLOCKWISE);
Curve_2 cv2 = Curve_2(circ2);
Arrangement_2 arr;
insert(arr, cv1);
insert(arr, cv2);
for (auto fit = arr.faces_begin(); fit != arr.faces_end(); ++fit)
{
if (fit->is_unbounded())
std::cout << "Unbounded face.\n";
else {
Arrangement_2::Ccb_halfedge_circulator curr, start;
start = curr = fit->outer_ccb();
do {
std::cout << " source --> " << curr->source()->point() << "\n";
std::cout << " target --> " << curr->target()->point() << "\n";
++curr;
} while (curr != start);
std::cout << std::endl;
}
}
return 0;
}