diff --git a/src/__private__/__edge_r.scad b/src/__private__/__edge_r.scad
new file mode 100644
index 00000000..70a6888d
--- /dev/null
+++ b/src/__private__/__edge_r.scad
@@ -0,0 +1,7 @@
+function __edge_r_begin(orig_r, a, a_step, m) =
+    let(leng = orig_r * cos(a_step / 2))
+    leng / cos((m - 0.5) * a_step - a);
+
+function __edge_r_end(orig_r, a, a_step, n) =      
+    let(leng = orig_r * cos(a_step / 2))    
+    leng / cos((n + 0.5) * a_step - a);
\ No newline at end of file
diff --git a/src/__private__/__shape_arc.scad b/src/__private__/__shape_arc.scad
index 404e1ac7..35959f6a 100644
--- a/src/__private__/__shape_arc.scad
+++ b/src/__private__/__shape_arc.scad
@@ -1,11 +1,3 @@
-function __edge_r_begin(orig_r, a, a_step, m) =
-    let(leng = orig_r * cos(a_step / 2))
-    leng / cos((m - 0.5) * a_step - a);
-
-function __edge_r_end(orig_r, a, a_step, n) =      
-    let(leng = orig_r * cos(a_step / 2))    
-    leng / cos((n + 0.5) * a_step - a);
-
 function __shape_arc(radius, angle, width, width_mode = "LINE_CROSS") =
     let(
         w_offset = width_mode == "LINE_CROSS" ? [width / 2, -width / 2] : (
diff --git a/src/arc.scad b/src/arc.scad
index 5b9d6658..d888ef66 100644
--- a/src/arc.scad
+++ b/src/arc.scad
@@ -15,6 +15,7 @@
 include <__private__/__frags.scad>;
 include <__private__/__is_vector.scad>;
 include <__private__/__ra_to_xy.scad>;
+include <__private__/__edge_r.scad>;
 include <__private__/__shape_arc.scad>;
 
 module arc(radius, angle, width, width_mode = "LINE_CROSS") {
diff --git a/src/arc_path.scad b/src/arc_path.scad
index 1b4bf38e..4f5a2bc7 100644
--- a/src/arc_path.scad
+++ b/src/arc_path.scad
@@ -15,14 +15,7 @@
 include <__private__/__frags.scad>;
 include <__private__/__is_vector.scad>;
 include <__private__/__ra_to_xy.scad>;
-
-function __edge_r_begin(orig_r, a, a_step, m) =
-    let(leng = orig_r * cos(a_step / 2))
-    leng / cos((m - 0.5) * a_step - a);
-
-function __edge_r_end(orig_r, a, a_step, n) =      
-    let(leng = orig_r * cos(a_step / 2))    
-    leng / cos((n + 0.5) * a_step - a);
+include <__private__/__edge_r.scad>;
 
 function arc_path(radius, angle) =
     let(
@@ -35,5 +28,6 @@ function arc_path(radius, angle) =
             m > n ? [] : [
                 for(i = [m:n]) 
                     __ra_to_xy(radius, a_step * i)
-            ])
+            ],
+            angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(radius, angles[1], a_step, n), angles[1])])
     ) points;
\ No newline at end of file