diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Ray_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Ray_3_do_intersect.h
index 45a2f9dd9fb..cf334475335 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Ray_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Ray_3_Ray_3_do_intersect.h
@@ -36,8 +36,8 @@ do_intersect(const typename K::Ray_3& r1,
 
   typename K::Coplanar_orientation_3 pred = k.coplanar_orientation_3_object();
 
-  CGAL::Orientation p0p1s = pred(r1.point(0), r1.point(1), r2.source());
-  CGAL::Orientation stp0 = pred(r2.source(), r2.second_point(), r1.point(0));
+  CGAL::Orientation p0p1s = pred(r1.source(), r1.second_point(), r2.source());
+  CGAL::Orientation stp0 = pred(r2.source(), r2.second_point(), r1.source());
 
   if(p0p1s == COLLINEAR)
   {
@@ -49,7 +49,7 @@ do_intersect(const typename K::Ray_3& r1,
   }
 
   if(stp0 == COLLINEAR)
-    return Ray_3_has_on_collinear_Point_3(r2, r1.point(0), k);
+    return Ray_3_has_on_collinear_Point_3(r2, r1.source(), k);
 
   return (p0p1s != stp0);
 }
diff --git a/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp
index e67bd82de7f..e1d603d4a5e 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp
@@ -72,6 +72,7 @@ public:
     check_no_intersection  (R(p(0,0,0), p(1,0,0)), R(p(1,-1,0), p(1,-2,0)));
     check_no_intersection  (R(p(0,0,0), p(1,0,0)), R(p(0,-1,0), p(0,-2,0)));
     check_no_intersection  (R(p(0,0,0), p(1,0,0)), R(p(0,1,0), p(0,2,0)));
+    check_no_intersection  (R(p(0,0,0), p(1,0,0)), R(p(-1,0,0), p(-1,-1,0)));
 
     // Point
     check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(0,0,0), p(-1,0,0)),
@@ -88,11 +89,10 @@ public:
                             p(1,0,0));
 
     // Segment
-    // @fixme
-//    check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(2,0,0), p(-3,0,0)),
-//                            S(p(0,0,0), p(2,0,0)));
-//    check_intersection     (R(p(2,0,0), p(-3,0,0)), R(p(0,0,0), p(1,0,0)),
-//                            S(p(2,0,0), p(0,0,0)));
+    check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(2,0,0), p(-3,0,0)),
+                            S(p(0,0,0), p(2,0,0)), false);
+    check_intersection     (R(p(2,0,0), p(-3,0,0)), R(p(0,0,0), p(1,0,0)),
+                            S(p(2,0,0), p(0,0,0)), false);
 
     // Ray
     check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(-1,0,0), p(3,0,0)),
diff --git a/Intersections_3/test/Intersections_3/test_intersections_Sphere_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_Sphere_3.cpp
index a4a2e255d86..62ecc427419 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_Sphere_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_Sphere_3.cpp
@@ -171,9 +171,8 @@ int main(int, char**)
   std::cout << " |||||||| Test Simple_cartesian<double> ||||||||" << std::endl;
   Sphere_3_intersection_tester< CGAL::Simple_cartesian<double> >(r).run();
 
-  // @fixme illegal Plane_3 constructor in Cartesian_kernel::Construct_radical_plane_3
-//  std::cout << " |||||||| Test CGAL::Homogeneous<CGAL::MP_Float> ||||||||" << std::endl;
-//  Sphere_3_intersection_tester< CGAL::Homogeneous<CGAL::MP_Float> >(r).run();
+  std::cout << " |||||||| Test CGAL::Homogeneous<CGAL::MP_Float> ||||||||" << std::endl;
+  Sphere_3_intersection_tester< CGAL::Homogeneous<CGAL::MP_Float> >(r).run();
 
   std::cout << " |||||||| Test EPICK ||||||||" << std::endl;
   Sphere_3_intersection_tester< CGAL::Epick >(r, true /*exact predicates*/).run();
@@ -181,8 +180,8 @@ int main(int, char**)
   std::cout << " |||||||| Test EPECK ||||||||" << std::endl;
   Sphere_3_intersection_tester< CGAL::Epeck >(r, true /*exact predicates*/, true /*exact constructions*/).run();
 
-//  std::cout << " |||||||| Test CGAL::Homogeneous<CGAL::Epeck_ft> ||||||||" << std::endl;
-//  Sphere_3_intersection_tester< CGAL::Homogeneous<CGAL::Epeck_ft> >(r, true /*exact predicates*/, true /*exact constructions*/).run();
+  std::cout << " |||||||| Test CGAL::Homogeneous<CGAL::Epeck_ft> ||||||||" << std::endl;
+  Sphere_3_intersection_tester< CGAL::Homogeneous<CGAL::Epeck_ft> >(r, true /*exact predicates*/, true /*exact constructions*/).run();
 
   std::cout << "OK!" << std::endl;
 }