diff --git a/Inscribed_areas/doc/Inscribed_areas/CGAL/Largest_empty_iso_rectangle_2.h b/Inscribed_areas/doc/Inscribed_areas/CGAL/Largest_empty_iso_rectangle_2.h
index f11af4ccdf1..080fc203bfb 100644
--- a/Inscribed_areas/doc/Inscribed_areas/CGAL/Largest_empty_iso_rectangle_2.h
+++ b/Inscribed_areas/doc/Inscribed_areas/CGAL/Largest_empty_iso_rectangle_2.h
@@ -142,9 +142,11 @@ Iso_rectangle_2 get_bounding_box();
 /// @{
 
 /*!
-Inserts point `p` in the point set, if it is not already in the set.
+Inserts point `p` in the point set, if it is not already in the set
+and on the bounded side of the bounding rectangle.
+\note Points on the boundary can be ignored as they lead to the same result.
 */
-void
+bool
 insert(const Point_2& p);
 
 /*!
diff --git a/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp b/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp
index 5128e958d84..bbf8989b7b8 100644
--- a/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp
+++ b/Inscribed_areas/examples/Inscribed_areas/largest_empty_rectangle.cpp
@@ -1,8 +1,7 @@
 #include <CGAL/Simple_cartesian.h>
-#include <CGAL/Iso_rectangle_2.h>
 #include <CGAL/Largest_empty_iso_rectangle_2.h>
 
-#include <fstream>
+#include <iostream>
 
 typedef double                                 Number_Type;
 typedef CGAL::Simple_cartesian<Number_Type>    K;
diff --git a/Inscribed_areas/include/CGAL/Largest_empty_iso_rectangle_2.h b/Inscribed_areas/include/CGAL/Largest_empty_iso_rectangle_2.h
index 95391cd85a5..4ef236892ab 100644
--- a/Inscribed_areas/include/CGAL/Largest_empty_iso_rectangle_2.h
+++ b/Inscribed_areas/include/CGAL/Largest_empty_iso_rectangle_2.h
@@ -762,7 +762,7 @@ bool
 Largest_empty_iso_rectangle_2<T>::insert(const Point_2& _p)
 {
   // check that the point is inside the bounding box
-  if(bbox_p.has_on_unbounded_side(_p)) {
+  if(! bbox_p.has_on_bounded_side(_p)) {
     return(false);
   }