diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_2.h
index 063c7b0a781..d146276263a 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_2.h
@@ -173,7 +173,7 @@ namespace CGALi {
 	typedef std::vector<CGAL::Object > solutions_container;
 	
 	solutions_container solutions;
-	CGAL::intersect_2<CK>( c, c1, std::back_inserter(solutions) );
+	intersection( c, c1, std::back_inserter(solutions) );
 	typename solutions_container::iterator it = solutions.begin();
 
 	CGAL_kernel_precondition( it != solutions.end() );
diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circle_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circle_2.h
index 6a211377b1d..52d115f7b76 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circle_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circle_2.h
@@ -37,7 +37,7 @@ circle_intersect( const typename CK::Circle_2 & c1,
   typedef std::vector<CGAL::Object > solutions_container;
   solutions_container solutions;
   
-  CGAL::intersect_2<CK>( c1, c2, std::back_inserter(solutions) );
+  intersection( c1, c2, std::back_inserter(solutions) );
   
   typename solutions_container::iterator it = solutions.begin();
   
diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circular_arc_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circular_arc_2.h
index bab2a0d18b8..cc2ed52d5ab 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circular_arc_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circular_arc_2.h
@@ -725,7 +725,7 @@ namespace CircularFunctors {
          (a1,a2,solutions)) {
 #endif
 
-      CGAL::intersect_2<CK> ( a1.supporting_circle(), a2.supporting_circle(),
+      intersection( a1.supporting_circle(), a2.supporting_circle(),
         std::back_inserter(solutions) );
 
 #ifdef CGAL_INTERSECTION_MAP_FOR_SUPPORTING_CIRCLES
diff --git a/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h b/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h
index 68907e9fc92..4e76d7ad86c 100644
--- a/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h
+++ b/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h
@@ -38,25 +38,15 @@ get_equation(const Circle_2<CK> & c)
 template< class CK >
 inline
 Circle_2<CK>
-construct_circle_2(const typename CK::Polynomial_for_circles_2_2 & eq)
+construct_circle(const typename CK::Polynomial_for_circles_2_2 & eq)
 {
   return CK().construct_circle_2_object()(eq);
 }
 
-template< class CK, class OutputIterator>
-inline
-OutputIterator
-intersect_2( const Circle_2<CK> & c1,
-			   const Circle_2<CK> & c2,
-			   OutputIterator res )
-{
-  return CK().intersect_2_object()(c1,c2,res);
-}
-
 template< class CK >
 inline
 bool
-has_on_2(const Circle_2<CK> &c, const Circular_arc_point_2<CK> &p)
+has_on(const Circle_2<CK> &c, const Circular_arc_point_2<CK> &p)
 {
   return CK().has_on_2_object()(c, p);
 }
diff --git a/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h b/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h
index f9dc1cc0095..126388c5783 100644
--- a/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h
+++ b/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h
@@ -38,22 +38,11 @@ get_equation(const Line_2<CK> & l)
 template< class CK >
 inline
 CGAL::Line_2<CK>
-construct_line_2(const typename CK::Polynomial_1_2 & eq)
+construct_line(const typename CK::Polynomial_1_2 & eq)
 {
   return CK().construct_line_2_object()(eq);
 }
 
-template< class CK, class OutputIterator>
-inline
-OutputIterator
-intersect_2( const Line_2<CK> & l,
-			   const Circle_2<CK> & c,
-			   OutputIterator res )
-{
-  return CK().intersect_2_object()(l,c,res);
-}
-
-
 CGAL_END_NAMESPACE
 
 #endif // CGAL_CIRCULAR_KERNEL_GLOBAL_FUNCTIONS_ON_LINE_2_H