diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 2f15ce3be76..0d67815ab7d 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -4716,22 +4716,30 @@ namespace HomogeneousKernelFunctors {
     {
       typename K::Construct_source_2 source;
       typename K::Construct_target_2 target;
+      typename K::Construct_vertex_2 vertex;
       typename K::Construct_circumcenter_2 circumcenter;
       typename K::Orientation_2 orientation;
 
-      const Point_2 a = source(s);
-      const Point_2 b = target(s);
+      const Point_2& a = source(s);
+      const Point_2& b = target(s);
+      CGAL_assertion(a != b);
+
+      const Point_2& p0 = vertex(t, 0);
+      const Point_2& p1 = vertex(t, 1);
+      const Point_2& p2 = vertex(t, 2);
+      CGAL_assertion(p0 != p1 && p1 != p2 && p2 != p0);
+
       const Point_2 cc = circumcenter(t);
 
       CGAL::Orientation o_abc = orientation(a, b, cc);
       if (o_abc == CGAL::COLLINEAR)
         return CGAL::ON_ORIENTED_BOUNDARY;
 
-      CGAL::Orientation o_abt = orientation(a, b, t[0]);
+      CGAL::Orientation o_abt = orientation(a, b, p0);
       if (o_abt == CGAL::COLLINEAR)
-        o_abt = orientation(a, b, t[1]);
+        o_abt = orientation(a, b, p1);
       if (o_abt == CGAL::COLLINEAR)
-        o_abt = orientation(a, b, t[2]);
+        o_abt = orientation(a, b, p2);
       CGAL_assertion(o_abt != CGAL::COLLINEAR);
 
       if (o_abc == o_abt) return CGAL::ON_POSITIVE_SIDE;