diff --git a/include/boost/geometry/extensions/algorithms/buffer/buffered_piece_collection.hpp b/include/boost/geometry/extensions/algorithms/buffer/buffered_piece_collection.hpp
index bd2cb6b44..a5ed513fd 100644
--- a/include/boost/geometry/extensions/algorithms/buffer/buffered_piece_collection.hpp
+++ b/include/boost/geometry/extensions/algorithms/buffer/buffered_piece_collection.hpp
@@ -81,7 +81,7 @@ struct check_original<polygon_tag>
     static inline int apply(Point const& point, Geometry const& geometry,
                             DistanceStrategy const& )
     {
-        return geometry::within(point, geometry) ? 1 : -1;
+        return geometry::covered_by(point, geometry) ? 1 : -1;
     }
 };
 
diff --git a/include/boost/geometry/extensions/algorithms/buffer/multi_buffer_inserter.hpp b/include/boost/geometry/extensions/algorithms/buffer/multi_buffer_inserter.hpp
index 240e86aa6..906ea8f33 100644
--- a/include/boost/geometry/extensions/algorithms/buffer/multi_buffer_inserter.hpp
+++ b/include/boost/geometry/extensions/algorithms/buffer/multi_buffer_inserter.hpp
@@ -31,7 +31,7 @@ struct check_original<multi_polygon_tag>
     template <typename Point, typename Geometry, typename DistanceStrategy>
     static inline int apply(Point const& point, Geometry const& geometry, DistanceStrategy const& distance_strategy)
     {
-        return geometry::within(point, geometry) ? 1 : -1;
+        return geometry::covered_by(point, geometry) ? 1 : -1;
     }
 };