diff --git a/crates/engine/src/cmd/modify/trim.rs b/crates/engine/src/cmd/modify/trim.rs
index 66eab0be8..9f8e856dd 100644
--- a/crates/engine/src/cmd/modify/trim.rs
+++ b/crates/engine/src/cmd/modify/trim.rs
@@ -283,6 +283,28 @@ pub(super) fn param_on(s: &Segment, p: Vec2) -> f64 {
     }
 }
 
+/// A polyline arc segment on `ga`'s circle that ends at `end` after turning through `sweep`
+/// (signed, positive counterclockwise), run on round the circle to the nearest boundary edge: the
+/// new end point and the segment's new bulge. `None` when no edge crosses the rest of the circle.
+fn extend_arc_segment(ga: &Arc, end: Vec2, sweep: f64, cut: &[Segment]) -> Option<(Vec2, f64)> {
+    let full = Segment::Arc { arc: Arc { start: 0.0, end: TAU - 1e-12, ..*ga }, ccw: true };
+    let a_end = ga.center.angle_to(end);
+    let ccw = sweep > 0.0;
+    // How far past `end` each crossing is, turning the way the segment turns; crossings on the
+    // segment itself (the last |sweep| of a turn) are not ahead of it.
+    let (x, more) = cut
+        .iter()
+        .flat_map(|c| intersect_ext(&full, c, false))
+        .map(|x| {
+            let a = ga.center.angle_to(x);
+            (x, norm_angle(if ccw { a - a_end } else { a_end - a }))
+        })
+        .filter(|(_, more)| *more > 1e-9 && *more + sweep.abs() < TAU - 1e-9)
+        .min_by(|a, b| a.1.total_cmp(&b.1))?;
+    let total = sweep.abs() + more;
+    Some((x, cadcraft_geom::arc_to_bulge(if ccw { total } else { -total })))
+}
+
 /// Extend the end of `h` nearest `pick` to the nearest boundary edge.
 pub(crate) fn extend(s: &mut Session, h: Handle, pick: Vec2, edges: Edges) -> Result<()> {
     if crate::cmd::curves::is_locked(s, h) {
@@ -326,18 +348,34 @@ pub(crate) fn extend(s: &mut Session, h: Handle, pick: Vec2, edges: Edges) -> Re
             let (i_end, i_prev) = if from_end { (n - 1, n - 2) } else { (0, 1) };
             let end = vs.get(i_end).map(|v| v.p).unwrap_or_default();
             let prev = vs.get(i_prev).map(|v| v.p).unwrap_or_default();
-            let dir = (end - prev).normalized();
-            let ray = Segment::Line(Line::new(end, end + dir * 1e8));
-            let np = cut
-                .iter()
-                .flat_map(|c| intersect_ext(&ray, c, false))
-                .filter(|x| (*x - end).dot(dir) > 1e-9)
-                .min_by(|x, y| x.dist(end).total_cmp(&y.dist(end)))
-                .ok_or_else(|| EngineError::Other("Object does not intersect an edge.".into()))?;
-            if let Some(v) = vs.get_mut(i_end) {
-                v.p = np;
+            // The end segment's bulge, signed for travel from `prev` out to `end`.
+            let i_seg = if from_end { i_prev } else { i_end };
+            let bulge = vs.get(i_seg).map_or(0.0, |v| if from_end { v.bulge } else { -v.bulge });
+            let none = || EngineError::Other("Object does not intersect an edge.".into());
+            if let Some((ga, _)) = cadcraft_geom::bulge_to_arc(prev, end, bulge) {
+                // An arc end segment runs on round its circle, as an arc does.
+                let (np, b) = extend_arc_segment(&ga, end, 4.0 * bulge.atan(), &cut).ok_or_else(none)?;
+                if let Some(v) = vs.get_mut(i_end) {
+                    v.p = np;
+                }
+                if let Some(v) = vs.get_mut(i_seg) {
+                    v.bulge = if from_end { b } else { -b };
+                }
+            } else {
+                let dir = (end - prev).normalized();
+                let ray = Segment::Line(Line::new(end, end + dir * 1e8));
+                let np = cut
+                    .iter()
+                    .flat_map(|c| intersect_ext(&ray, c, false))
+                    .filter(|x| (*x - end).dot(dir) > 1e-9)
+                    .min_by(|x, y| x.dist(end).total_cmp(&y.dist(end)))
+                    .ok_or_else(none)?;
+                if let Some(v) = vs.get_mut(i_end) {
+                    v.p = np;
+                }
             }
-            lwpoly(vs, false)
+            // Width, elevation and linetype generation stay as they were.
+            EntityKind::LwPolyline(cadcraft_doc::LwPolyline { vertices: vs, ..p.clone() })
         }
         k => crate::cmd::modify2::extend_other(k, &cut, pick)?,
     };
diff --git a/crates/engine/tests/it/extend_polyline_arc_end.rs b/crates/engine/tests/it/extend_polyline_arc_end.rs
new file mode 100644
index 000000000..496187767
--- /dev/null
+++ b/crates/engine/tests/it/extend_polyline_arc_end.rs
@@ -0,0 +1,137 @@
+//! EXTEND on an open polyline whose end segment is an arc: the arc runs on round its own circle
+//! to the boundary, as EXTEND does with an ARC, instead of the end vertex sliding along the chord
+//! with the old bulge (which changed the arc's radius and centre, or missed the boundary). The
+//! polyline keeps its width, elevation and linetype generation.
+
+use cadcraft_engine::Session;
+use cadcraft_engine::doc::{Common, Entity, EntityKind, Handle, LwPolyline};
+use cadcraft_engine::geom::{PolyVertex, Vec2};
+use serde_json::json;
+
+const TOL: f64 = 1e-9;
+
+fn add(s: &mut Session, kind: EntityKind) -> String {
+    let space = s.space();
+    let d = s.doc_mut().unwrap();
+    let handle = d.new_handle();
+    d.space_mut(&space).unwrap().push(Entity { handle, common: Common::default(), kind });
+    handle.hex()
+}
+
+fn v(x: f64, y: f64, bulge: f64) -> PolyVertex {
+    PolyVertex { p: Vec2::new(x, y), bulge, ..Default::default() }
+}
+
+fn pline(vertices: Vec<PolyVertex>) -> LwPolyline {
+    LwPolyline { vertices, closed: false, const_width: 0.0, elevation: 0.0, plinegen: false }
+}
+
+fn edge(s: &mut Session, a: [f64; 2], b: [f64; 2]) -> String {
+    let r = s.execute("line", &json!({ "points": [a, b] })).unwrap();
+    r["handles"][0].as_str().unwrap().to_string()
+}
+
+fn polyline(s: &Session, h: &str) -> LwPolyline {
+    match &s.doc().unwrap().entity(Handle::parse_hex(h).unwrap()).unwrap().kind {
+        EntityKind::LwPolyline(p) => p.clone(),
+        k => panic!("not a polyline: {k:?}"),
+    }
+}
+
+fn near(a: Vec2, x: f64, y: f64) -> bool {
+    (a.x - x).abs() < 1e-6 && (a.y - y).abs() < 1e-6
+}
+
+/// tan(22.5°): the bulge of a quarter circle.
+fn quarter() -> f64 {
+    (std::f64::consts::PI / 8.0).tan()
+}
+
+/// The bulge of an arc turning through `deg` degrees (positive counterclockwise).
+fn bulge(deg: f64) -> f64 {
+    (deg.to_radians() / 4.0).tan()
+}
+
+#[test]
+fn a_counterclockwise_arc_at_the_end_runs_on_round_its_circle() {
+    let mut s = Session::new();
+    let e = edge(&mut s, [-50.0, -5.0], [50.0, -5.0]);
+    // A line in from (20,0), then a quarter circle about the origin from (10,0) to (0,10).
+    let mut pl = pline(vec![v(20.0, 0.0, 0.0), v(10.0, 0.0, quarter()), v(0.0, 10.0, 0.0)]);
+    pl.const_width = 0.5;
+    pl.elevation = 3.0;
+    pl.plinegen = true;
+    let h = add(&mut s, EntityKind::LwPolyline(pl));
+    s.execute("extend", &json!({ "handle": h, "pick": [0.5, 9.9], "edges": [e] })).unwrap();
+    let p = polyline(&s, &h);
+    assert_eq!(p.vertices.len(), 3);
+    // Round the circle (radius 10) through (-10,0) to y = -5: a 210° turn in all.
+    let end = p.vertices[2].p;
+    assert!(near(end, -(75.0f64.sqrt()), -5.0), "end {end:?}");
+    assert!((p.vertices[1].bulge - bulge(210.0)).abs() < TOL, "bulge {}", p.vertices[1].bulge);
+    assert!(near(p.vertices[0].p, 20.0, 0.0) && near(p.vertices[1].p, 10.0, 0.0));
+    assert_eq!((p.const_width, p.elevation, p.plinegen), (0.5, 3.0, true));
+}
+
+#[test]
+fn an_arc_at_the_start_runs_on_backwards_round_its_circle() {
+    let mut s = Session::new();
+    let e = edge(&mut s, [-50.0, -5.0], [50.0, -5.0]);
+    // The same path drawn the other way: clockwise from (0,10) to (10,0), then out to (20,0).
+    let h = add(&mut s, EntityKind::LwPolyline(pline(vec![v(0.0, 10.0, -quarter()), v(10.0, 0.0, 0.0), v(20.0, 0.0, 0.0)])));
+    s.execute("extend", &json!({ "handle": h, "pick": [0.5, 9.9], "edges": [e] })).unwrap();
+    let p = polyline(&s, &h);
+    assert!(near(p.vertices[0].p, -(75.0f64.sqrt()), -5.0), "start {:?}", p.vertices[0].p);
+    assert!((p.vertices[0].bulge + bulge(210.0)).abs() < TOL, "bulge {}", p.vertices[0].bulge);
+    assert!(near(p.vertices[1].p, 10.0, 0.0) && near(p.vertices[2].p, 20.0, 0.0));
+}
+
+#[test]
+fn a_clockwise_arc_at_the_end_runs_on_clockwise() {
+    let mut s = Session::new();
+    let e = edge(&mut s, [-50.0, 5.0], [50.0, 5.0]);
+    // Clockwise about the origin from (10,0) to (0,-10); on round through (-10,0) to y = 5.
+    let h = add(&mut s, EntityKind::LwPolyline(pline(vec![v(20.0, 0.0, 0.0), v(10.0, 0.0, -quarter()), v(0.0, -10.0, 0.0)])));
+    s.execute("extend", &json!({ "handle": h, "pick": [0.5, -9.9], "edges": [e] })).unwrap();
+    let p = polyline(&s, &h);
+    assert!(near(p.vertices[2].p, -(75.0f64.sqrt()), 5.0), "end {:?}", p.vertices[2].p);
+    assert!((p.vertices[1].bulge + bulge(210.0)).abs() < TOL, "bulge {}", p.vertices[1].bulge);
+}
+
+#[test]
+fn the_nearest_crossing_ahead_on_the_circle_wins() {
+    let mut s = Session::new();
+    // A boundary crossing the circle twice ahead of the end: x = -6 at about 127° and 233°.
+    let e = edge(&mut s, [-6.0, -50.0], [-6.0, 50.0]);
+    let h = add(&mut s, EntityKind::LwPolyline(pline(vec![v(20.0, 0.0, 0.0), v(10.0, 0.0, quarter()), v(0.0, 10.0, 0.0)])));
+    s.execute("extend", &json!({ "handle": h, "pick": [0.5, 9.9], "edges": [e] })).unwrap();
+    let p = polyline(&s, &h);
+    assert!(near(p.vertices[2].p, -6.0, 8.0), "end {:?}", p.vertices[2].p);
+    let turn = 8.0f64.atan2(-6.0).to_degrees();
+    assert!((p.vertices[1].bulge - bulge(turn)).abs() < TOL, "bulge {}", p.vertices[1].bulge);
+}
+
+#[test]
+fn an_arc_end_whose_circle_misses_every_edge_is_left_alone() {
+    let mut s = Session::new();
+    // The chord (10,0)→(0,10) runs on to this edge, but the circle never reaches it.
+    let e = edge(&mut s, [-50.0, 30.0], [50.0, 30.0]);
+    let before = pline(vec![v(20.0, 0.0, 0.0), v(10.0, 0.0, quarter()), v(0.0, 10.0, 0.0)]);
+    let h = add(&mut s, EntityKind::LwPolyline(before.clone()));
+    assert!(s.execute("extend", &json!({ "handle": h, "pick": [0.5, 9.9], "edges": [e] })).is_err());
+    assert_eq!(polyline(&s, &h), before);
+}
+
+#[test]
+fn a_straight_end_keeps_the_polyline_width_and_elevation() {
+    let mut s = Session::new();
+    let e = edge(&mut s, [50.0, -50.0], [50.0, 50.0]);
+    let mut pl = pline(vec![v(0.0, 0.0, 0.0), v(10.0, 0.0, 0.0)]);
+    pl.const_width = 0.5;
+    pl.elevation = 3.0;
+    let h = add(&mut s, EntityKind::LwPolyline(pl));
+    s.execute("extend", &json!({ "handle": h, "pick": [9.0, 0.0], "edges": [e] })).unwrap();
+    let p = polyline(&s, &h);
+    assert!(near(p.vertices[1].p, 50.0, 0.0), "end {:?}", p.vertices[1].p);
+    assert_eq!((p.const_width, p.elevation), (0.5, 3.0));
+}
diff --git a/crates/engine/tests/it/main.rs b/crates/engine/tests/it/main.rs
index 38fb4d005..b6ec02d60 100644
--- a/crates/engine/tests/it/main.rs
+++ b/crates/engine/tests/it/main.rs
@@ -46,6 +46,7 @@ mod draworder;
 mod dyn_input;
 mod dynamic_block_data;
 mod dynamic_grips;
+mod extend_polyline_arc_end;
 mod fillet_chamfer;
 mod fix_holds_grips;
 mod followups_626;