diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index d37e412ee40..19d29f76557 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -4322,18 +4322,13 @@ namespace CartesianKernelFunctors {
       const Point_2& p2 = vertex(t, 2);
       CGAL_assertion(p0 != p1 && p1 != p2 && p2 != p0);
 
-      const FT dX = b.x() - a.x();
-      const FT dY = b.y() - a.y();
-      const FT R0 = p0.x() * p0.x() + p0.y() * p0.y();
-      const FT R1 = p1.x() * p1.x() + p1.y() * p1.y();
-      const FT R2 = p2.x() * p2.x() + p2.y() * p2.y();
-      const FT denominator = (p1.x() - p0.x()) * (p2.y() - p0.y()) +
-                             (p0.x() - p2.x()) * (p1.y() - p0.y());
-      const FT det = 2 * denominator * (a.x() * dY - a.y() * dX)
-                       - (R2 - R1) * (p0.x() * dX + p0.y() * dY)
-                       - (R0 - R2) * (p1.x() * dX + p1.y() * dY)
-                       - (R1 - R0) * (p2.x() * dX + p2.y() * dY);
-      return CGAL::sign(det);
+      return circumcenter_oriented_side_of_oriented_segmentC2(
+                  a.x(), a.y(),
+                  b.x(), b.y(),
+                  p0.x(), p0.y(),
+                  p1.x(), p1.y(),
+                  p2.x(), p2.y()
+      );
     }
   };
 
diff --git a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
index 7e49bb62376..e6da15d2547 100644
--- a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
+++ b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
@@ -708,6 +708,28 @@ power_side_of_oriented_power_circleC2(const FT &px, const FT &py, const FT &pwt,
   return cmpy * sign_of_determinant(dpy, dpz, dqy, dqz);
 }
 
+template <class FT>
+Oriented_side
+circumcenter_oriented_side_of_oriented_segmentC2(const FT& ax,  const FT& ay,
+                                                 const FT& bx,  const FT& by,
+                                                 const FT& p0x, const FT& p0y,
+                                                 const FT& p1x, const FT& p1y,
+                                                 const FT& p2x, const FT& p2y)
+{
+  const FT dX = bx - ax;
+  const FT dY = bx - ay;
+  const FT R0 = p0x * p0x + p0x * p0x;
+  const FT R1 = p1x * p1x + p1x * p1x;
+  const FT R2 = p2x * p2x + p2x * p2x;
+  const FT denominator = (p1x - p0x) * (p2x - p0x) +
+                         (p0x - p2x) * (p1x - p0x);
+  const FT det = 2 * denominator * (ax * dY - ay * dX)
+                   - (R2 - R1) * (p0x * dX + p0x * dY)
+                   - (R0 - R2) * (p1x * dX + p1x * dY)
+                   - (R1 - R0) * (p2x * dX + p2x * dY);
+  return CGAL::sign(det);
+}
+
 } //namespace CGAL
 
 #endif  // CGAL_PREDICATES_KERNEL_FTC2_H