diff --git a/Circular_kernel_3/test/Circular_kernel_3/include/CGAL/_test_sphere_predicates.h b/Circular_kernel_3/test/Circular_kernel_3/include/CGAL/_test_sphere_predicates.h
index e173ce2f82d..385bb37470d 100644
--- a/Circular_kernel_3/test/Circular_kernel_3/include/CGAL/_test_sphere_predicates.h
+++ b/Circular_kernel_3/test/Circular_kernel_3/include/CGAL/_test_sphere_predicates.h
@@ -198,7 +198,92 @@ void _test_line_arc_equal(SK sk) {
       }
     }
   }
+}
 
+template <class SK>
+void _test_circular_arc_equal(SK sk) {
+
+  typedef typename SK::RT                               RT;
+  typedef typename SK::FT                               FT;
+  typedef typename SK::Root_of_2                        Root_of_2;
+  typedef typename SK::Circular_arc_point_3             Circular_arc_point_3;
+  typedef typename SK::Circular_arc_3                   Circular_arc_3;
+  typedef typename SK::Point_3                          Point_3;
+  typedef typename SK::Plane_3                          Plane_3;
+  typedef typename SK::Circle_3                         Circle_3;
+  typedef typename SK::Sphere_3                         Sphere_3;
+  typedef typename SK::Algebraic_kernel                 AK;
+  typedef typename SK::Get_equation                     Get_equation;
+  typedef typename SK::Equal_3                          Equal_3;
+  typedef typename SK::Construct_circle_3               Construct_circle_3;
+  typedef typename SK::Construct_sphere_3               Construct_sphere_3;
+  typedef typename SK::Construct_circular_arc_3         Construct_circular_arc_3;
+  typedef typename SK::Polynomials_for_circle_3         Polynomials_for_circle_3;
+  typedef typename AK::Polynomial_for_spheres_2_3       Polynomial_for_spheres_2_3;
+  typedef typename AK::Polynomial_1_3                   Polynomial_1_3;
+  typedef typename AK::Polynomials_for_line_3           Polynomials_for_line_3;
+  typedef typename AK::Root_for_spheres_2_3             Root_for_spheres_2_3;
+
+  Equal_3 theEqual_3 = sk.equal_3_object();
+  Get_equation theGet_equation = sk.get_equation_object();
+  Construct_circle_3 theConstruct_circle_3 = sk.construct_circle_3_object();
+  Construct_sphere_3 theConstruct_sphere_3 = sk.construct_sphere_3_object();
+  Construct_circular_arc_3 theConstruct_circular_arc_3 = sk.construct_circular_arc_3_object();
+
+  CGAL::Random generatorOfgenerator;
+  int random_seed = generatorOfgenerator.get_int(0, 123456);
+  CGAL::Random theRandom(random_seed);
+  int random_max = 127;
+  int random_min = -127; 
+
+  std::cout << "Testing Equal_3 for Circular_arc_3..." << std::endl;
+  for(int i=0; i<100; i++) {
+    int a,b,c,d,u,v,r;
+    FT x,y,z;
+    do {
+      a = theRandom.get_int(random_min,random_max);
+      b = theRandom.get_int(random_min,random_max);
+      c = theRandom.get_int(random_min,random_max);
+      d = theRandom.get_int(random_min,random_max);
+    } while((a == 0) && (b == 0) && (c == 0));
+    u = theRandom.get_int(random_min,random_max);
+    v = theRandom.get_int(random_min,random_max);
+    do {
+      r = theRandom.get_int(random_min,random_max);
+    } while(r <= 0);
+    if(a != 0) {
+      x = FT(-(b*u + c*v + d),a);
+      y = FT(u);
+      z = FT(v);
+    } else if(b != 0) {
+      x = FT(u);
+      y = FT(-(a*u + c*v + d),b);
+      z = FT(v);
+    } else {
+      x = FT(u);
+      y = FT(v);
+      z = FT(-(a*u + b*v + d),c);
+    } 
+    const Plane_3 plane = Plane_3(a,b,c,d);
+    const Plane_3 plane2 = Plane_3(2*a,2*b,2*c,2*d);
+    const FT sqr = FT(r);
+    const Point_3 p = Point_3(x,y,z);
+    const Polynomials_for_circle_3 pfc = 
+      std::make_pair(Polynomial_for_spheres_2_3(x,y,z,r),
+                     Polynomial_1_3(a,b,c,d));
+    Circle_3 circle3 = theConstruct_circle_3(pfc);
+    Circle_3 circle = theConstruct_circle_3(p,sqr,plane);
+    Circular_arc_3 circle_arc3 = theConstruct_circular_arc_3(circle3);
+    Circular_arc_3 circle_arc = theConstruct_circular_arc_3(circle);
+    Circle_3 circle2 = theConstruct_circle_3(p,sqr,plane2);
+    Circular_arc_3 circle_arc2 = theConstruct_circular_arc_3(circle2);
+    assert(theEqual_3(circle_arc,circle_arc2));
+    assert(theEqual_3(circle_arc,circle_arc3));
+    Circular_arc_3 cother = circle_arc2;
+    assert(theEqual_3(circle_arc,cother));
+    assert(cother.rep().is_full());
+    // When the !if_full(), we use the compare of circular_arc_point, already tested
+  }
 }
 
 template <class SK>
@@ -487,6 +572,7 @@ void _test_spherical_kernel_predicates(SK sk)
   _test_circular_arc_point_equal(sk);
   _test_circle_equal(sk);
   _test_line_arc_equal(sk);
+  _test_circular_arc_equal(sk);
   _test_has_on_predicate(sk);
   _test_do_overlap_predicate(sk);
   std::cout << "All tests on predicates are OK." << std::endl;