diff --git a/Distance_3/test/Distance_3/test_distance_3.cpp b/Distance_3/test/Distance_3/test_distance_3.cpp
index 7af9351110c..ab67ad18d79 100644
--- a/Distance_3/test/Distance_3/test_distance_3.cpp
+++ b/Distance_3/test/Distance_3/test_distance_3.cpp
@@ -208,6 +208,36 @@ private:
     check_squared_distance (p(1, 1, 1), t, 1);
     check_squared_distance (p(1, 0, 1), t, 1);
     check_squared_distance (p(0, 0, 1), t, 1);
+
+    // Degenerate
+    check_squared_distance (p(1, 2, 3), T(p(4,3,2), p(4,3,2), p(4,3,2)), squared_distance(p(1, 2, 3), p(4,3,2)));
+    check_squared_distance (p(1, 2, 3), T(p(4,3,2), p(10,12,3), p(4,3,2)), squared_distance(p(1, 2, 3), p(4,3,2)));
+    check_squared_distance (p(0, 0, 0), T(p(4,3,2), p(4,-3,-2), p(4,3,2)), squared_distance(p(0, 0, 0), p(4,0,0)));
+
+    // On the triangle
+    check_squared_distance (p(7, 1, -5), T(p(2,9,8), p(-4,-3,-5), p(7, 1, -5)), 0); // vertex
+    check_squared_distance (p(7, 1, -5), T(p(14,2,-10), p(-7,-1,5), p(8, 3, -1)), 0); // edge
+    check_squared_distance (p(1, 4, -3), T(p(0,-8,-3), p(-5,14,-3), p(10, 1, -3)), 0); // face
+
+    // General
+    check_squared_distance (p(-15, 1, 0), T(p(-10, 1, 0), p(0,0,0), p(10,0,0)), 25);
+    check_squared_distance (p(-5, 0, 0), T(p(-10, 1, 0), p(0,0,0), p(10,0,0)), squared_distance(p(-5, 0, 0), S(p(-10, 1, 0), p(0,0,0))));
+    check_squared_distance (p(0, -3, 0), T(p(-10, 1, 0), p(0,0,0), p(10,0,0)), 9);
+    check_squared_distance (p(3, -3, 0), T(p(-10, 1, 0), p(0,0,0), p(10,0,0)), squared_distance(p(3, -3, 0), S(p(0,0,0), p(10,0,0))));
+    check_squared_distance (p(16, 1, 1), T(p(-10, 1, 0), p(0,0,0), p(10,0,0)), 38);
+    check_squared_distance (p(5, 5, 2), T(p(-10, 1, 0), p(0,0,0), p(10,0,0)), squared_distance(p(5, 5, 2), S(p(10,0,0), p(-10,1,0))));
+
+    for(int i=0; i<N; ++i)
+    {
+      P p0 = random_point();
+      P p1 = random_point();
+      P p2 = random_point();
+      P q = random_point();
+
+      check_squared_distance_with_bound(q, T(p0, p1, p2), squared_distance(q, S(p0, p1)));
+      check_squared_distance_with_bound(q, T(p0, p1, p2), squared_distance(q, S(p1, p2)));
+      check_squared_distance_with_bound(q, T(p0, p1, p2), squared_distance(q, S(p2, p0)));
+    }
   }
 
   void P_Tet()