diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Plane_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Plane_3.h
index 38a119e1320..27509532ac7 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Plane_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Plane_3.h
@@ -169,7 +169,9 @@ inline
 typename PlaneC3<R>::Point_3
 PlaneC3<R>::point() const
 {
-  return point_on_plane(*this);
+  FT x, y, z;
+  point_on_planeC3(a(), b(), c(), d(), x, y, z);
+  return R().construct_point_3_object()(x, y, z);
 }
 
 template < class R >
@@ -178,7 +180,13 @@ typename PlaneC3<R>::Point_3
 PlaneC3<R>::
 projection(const typename PlaneC3<R>::Point_3 &p) const
 {
-  return projection_plane(p, *this);
+  FT x, y, z;
+  projection_planeC3(a(), b(), c(), d(),
+                     R().compute_x_3_object()(p),
+                     R().compute_y_3_object()(p),
+                     R().compute_z_3_object()(p),
+                     x, y, z);
+  return R().construct_point_3_object()(x, y, z);
 }
 
 template < class R >
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/basic_constructions_3.h b/Cartesian_kernel/include/CGAL/Cartesian/basic_constructions_3.h
index 1760074c988..f00c2ca8791 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/basic_constructions_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/basic_constructions_3.h
@@ -17,7 +17,6 @@
 #ifndef CGAL_CARTESIAN_BASIC_CONSTRUCTIONS_3_H
 #define CGAL_CARTESIAN_BASIC_CONSTRUCTIONS_3_H
 
-#include <CGAL/Cartesian/point_constructions_3.h>
 #include <CGAL/Cartesian/plane_constructions_3.h>
 #include <CGAL/Cartesian/ft_constructions_3.h>
 
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/point_constructions_3.h b/Cartesian_kernel/include/CGAL/Cartesian/point_constructions_3.h
deleted file mode 100644
index 80afbff35e1..00000000000
--- a/Cartesian_kernel/include/CGAL/Cartesian/point_constructions_3.h
+++ /dev/null
@@ -1,50 +0,0 @@
-// Copyright (c) 2000
-// Utrecht University (The Netherlands),
-// ETH Zurich (Switzerland),
-// INRIA Sophia-Antipolis (France),
-// Max-Planck-Institute Saarbruecken (Germany),
-// and Tel-Aviv University (Israel).  All rights reserved.
-//
-// This file is part of CGAL (www.cgal.org)
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
-//
-//
-// Author(s)     : Herve Bronnimann
-
-#ifndef CGAL_CARTESIAN_POINT_CONSTRUCTIONS_3_H
-#define CGAL_CARTESIAN_POINT_CONSTRUCTIONS_3_H
-
-#include <CGAL/Cartesian/Point_3.h>
-#include <CGAL/constructions/kernel_ftC3.h>
-
-namespace CGAL {
-
-template <class K>
-CGAL_KERNEL_LARGE_INLINE
-PointC3<K>
-point_on_plane(const PlaneC3<K> &p)
-{
-  typename K::FT x, y, z;
-  point_on_planeC3(p.a(), p.b(), p.c(), p.d(), x, y, z);
-  return PointC3<K>(x, y, z);
-}
-
-template <class K>
-CGAL_KERNEL_LARGE_INLINE
-PointC3<K>
-projection_plane(const PointC3<K> &p,
-                 const PlaneC3<K> &h)
-{
-  typename K::FT x, y, z;
-  projection_planeC3(h.a(), h.b(), h.c(), h.d(),
-                     p.x(), p.y(), p.z(),
-                     x, y, z);
-  return PointC3<K>(x, y, z);
-}
-
-} //namespace CGAL
-
-#endif // CGAL_CARTESIAN_POINT_CONSTRUCTIONS_3_H