diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Circle_2.h b/Cartesian_kernel/include/CGAL/Cartesian/Circle_2.h
index 22ca7a1cf29..fef594d6e17 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Circle_2.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Circle_2.h
@@ -26,6 +26,7 @@
 
 #include <CGAL/utility.h>
 #include <CGAL/Cartesian/predicates_on_points_2.h>
+#include <boost/tuple/tuple.hpp>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -38,7 +39,7 @@ class CircleC2
   typedef typename R_::Point_2              Point_2;
   typedef typename R_::Orientation          Orientation;
 
-  typedef Triple<Point_2, FT, Orientation>         Rep;
+  typedef boost::tuple<Point_2, FT, Orientation>   Rep;
   typedef typename R_::template Handle<Rep>::type  Base;
 
   Base base;
@@ -62,17 +63,17 @@ public:
 
   const Point_2 & center() const
   {
-    return get(base).first;
+    return get(base).get<0>();
   }
 
   const FT & squared_radius() const
   {
-    return get(base).second;
+    return get(base).get<1>();
   }
 
   Orientation orientation() const
   {
-    return get(base).third;
+    return get(base).get<2>();
   }
 
 };
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
index c079b14a033..147f8b91d82 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
@@ -27,6 +27,7 @@
 #include <CGAL/utility.h>
 #include <CGAL/Handle_for.h>
 #include <CGAL/Interval_nt.h>
+#include <boost/tuple/tuple.hpp>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -39,7 +40,7 @@ class SphereC3
   typedef typename R_::Sphere_3             Sphere_3;
   typedef typename R_::Circle_3             Circle_3;
 
-  typedef Triple<Point_3, FT, Orientation>         Rep;
+  typedef boost::tuple<Point_3, FT, Orientation>   Rep;
   typedef typename R_::template Handle<Rep>::type  Base;
 
   Base base;
@@ -106,17 +107,17 @@ public:
 
   const Point_3 & center() const
   {
-      return get(base).first;
+      return get(base).get<0>();
   }
   const FT & squared_radius() const
   {
       // Returns the square of the radius (instead of the radius itself,
       // which would require square roots)
-      return get(base).second;
+      return get(base).get<1>();
   }
   Orientation orientation() const
   {
-      return get(base).third;
+      return get(base).get<2>();
   }
 
   // A circle is degenerate if its (squared) radius is null or negative
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/CircleH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/CircleH2.h
index d0c3da5ad8a..423922ee8e7 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/CircleH2.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/CircleH2.h
@@ -28,6 +28,7 @@
 
 #include <CGAL/utility.h>
 #include <CGAL/Interval_nt.h>
+#include <boost/tuple/tuple.hpp>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -38,7 +39,7 @@ class CircleH2
     typedef typename R_::RT                   RT;
     typedef typename R_::Point_2              Point_2;
 
-    typedef Triple<Point_2, FT, Orientation>         Rep;
+    typedef boost::tuple<Point_2, FT, Orientation>   Rep;
     typedef typename R_::template Handle<Rep>::type  Base;
 
     Base base;
@@ -116,13 +117,13 @@ template <class R>
 inline
 const typename CircleH2<R>::Point_2 &
 CircleH2<R>::center() const
-{ return get(base).first; }
+{ return get(base).get<0>(); }
 
 template <class R>
 inline
 const typename CircleH2<R>::FT &
 CircleH2<R>::squared_radius() const
-{ return get(base).second; }
+{ return get(base).get<1>(); }
 
 template <class R>
 CGAL_KERNEL_INLINE
@@ -138,7 +139,7 @@ template <class R>
 inline
 Orientation
 CircleH2<R>::orientation() const
-{ return get(base).third; }
+{ return get(base).get<2>(); }
 
 template <class R>
 CGAL_KERNEL_INLINE
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
index 869cce61a13..96a5668f011 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/SphereH3.h
@@ -27,6 +27,7 @@
 #include <CGAL/utility.h>
 #include <CGAL/Interval_nt.h>
 #include <CGAL/Homogeneous/predicates_on_pointsH3.h>
+#include <boost/tuple/tuple.hpp>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -37,7 +38,7 @@ class SphereH3
    typedef typename R_::FT                   FT;
    typedef typename R_::Point_3              Point_3;
 
-   typedef Triple<Point_3, FT, Orientation>         Rep;
+   typedef boost::tuple<Point_3, FT, Orientation>   Rep;
    typedef typename R_::template Handle<Rep>::type  Base;
 
    Base base;
@@ -180,19 +181,19 @@ template <class R>
 inline
 const typename SphereH3<R>::Point_3 &
 SphereH3<R>::center() const
-{ return get(base).first; }
+{ return get(base).get<0>(); }
 
 template <class R>
 inline
 const typename SphereH3<R>::FT &
 SphereH3<R>::squared_radius() const
-{ return get(base).second; }
+{ return get(base).get<1>(); }
 
 template <class R>
 inline
 Orientation
 SphereH3<R>::orientation() const
-{ return get(base).third; }
+{ return get(base).get<2>(); }
 
 template <class R>
 inline