diff --git a/Triangulation_3/include/CGAL/predicates/predicates_on_weighted_points_cartesian_3.h b/Triangulation_3/include/CGAL/predicates/predicates_on_weighted_points_cartesian_3.h
index 830a39383ea..9155e1cd1e4 100644
--- a/Triangulation_3/include/CGAL/predicates/predicates_on_weighted_points_cartesian_3.h
+++ b/Triangulation_3/include/CGAL/predicates/predicates_on_weighted_points_cartesian_3.h
@@ -91,7 +91,7 @@ in_smallest_orthogonal_sphereC3(
   FT sq = spx*qpx + spy*qpy + spz*qpz;
   FT sr = spx*rpx + spy*rpy + spz*rpz;
 
-  CGAL_triangulation_assertion( ! CGAL_NTS is_zero(den) );
+  CGAL_assertion( ! CGAL_NTS is_zero(den) );
   // return  sign of (c- s)^2 - (c^2 - pw) - sw    note that den >= 0 -
   return CGAL_NTS sign( den*(ss - sw + pw)- detq*sq - detr*sr);
 }
@@ -172,7 +172,7 @@ does_simplex_intersect_weighted_dual_supportC3(
   FT dets = determinant(qq,qr,qpw,
 			      qr,rr,rpw,
 			      qs,rs,spw);
-  CGAL_triangulation_assertion( ! CGAL_NTS is_zero(den) );
+  CGAL_assertion( ! CGAL_NTS is_zero(den) );
 
 
   // The barycentrique coordinate of the smallest orthogonal sphere center
@@ -230,7 +230,7 @@ does_simplex_intersect_weighted_dual_supportC3(
   FT detr = determinant(qq,qpw,
 			      qr,rpw);
 
-  CGAL_triangulation_assertion( ! CGAL_NTS is_zero(den) );
+  CGAL_assertion( ! CGAL_NTS is_zero(den) );
 
    // The barycentrique coordinate of the smallest orthogonal sphere center
   // are  detq/2*den detr/2*den
diff --git a/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h b/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h
index a861fe9fb97..948ec6a3ee4 100644
--- a/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h
+++ b/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h
@@ -84,7 +84,6 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
   Weighted_point wp04(p0,18.);
   Weighted_point wp05(p0,24.);
 
-#if 0
   assert(does_simplex_intersect_dual_support(wp0,wp1,wp2,wp3) 
 	 == CGAL::ON_UNBOUNDED_SIDE);
 
@@ -124,7 +123,6 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
 	 ==  CGAL::ON_UNBOUNDED_SIDE);
   assert(does_simplex_intersect_dual_support(wp1,wp05)
 	 ==  CGAL::ON_UNBOUNDED_SIDE);
- #endif
 
   // test of Construct_weighted_circumcenter_3 and compare_power_distance
    std::cout << "test of Construct_weighted_circumcenter_3" << std::endl;
@@ -133,7 +131,7 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
   c = weighted_circumcenter(wp0,wp1,wp2,wp3);
 
   assert (compare_power_distance(c,wp0,wp1) == CGAL::EQUAL);
-#if 0
+
   assert (compare_power_distance(c,wp01,wp1) == CGAL::LARGER);
   assert (compare_power_distance(c,wp03,wp1) == CGAL::SMALLER);
 
@@ -298,5 +296,4 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
   assert(power_test(wq01,wq01) == CGAL::ON_ORIENTED_BOUNDARY);
   assert(power_test(wq01,wq02) == CGAL::ON_NEGATIVE_SIDE);
 
-#endif
 }