diff --git a/crates/engine/src/cmd/sketch_corner_tests.rs b/crates/engine/src/cmd/sketch_corner_tests.rs
new file mode 100644
index 00000000..344e8fea
--- /dev/null
+++ b/crates/engine/src/cmd/sketch_corner_tests.rs
@@ -0,0 +1,98 @@
+//! Sketch Fillet and Chamfer at corners (#46): line–line, line–arc and arc–arc corners, the
+//! corners of a constrained rectangle, several corners at once, and radii too large for the
+//! corner (a clear error that leaves the sketch as it was).
+
+use serde_json::{Value, json};
+
+use crate::Session;
+
+fn new_sketch() -> Session {
+    let mut s = Session::default();
+    s.execute("sketch.create", &json!({"plane": "XY"})).unwrap();
+    s
+}
+
+fn run(s: &mut Session, id: &str, p: Value) -> Value {
+    match s.execute(id, &p) {
+        Ok(v) => v,
+        Err(e) => panic!("{id} {p}: {e}"),
+    }
+}
+
+fn curves(r: &Value) -> Vec<String> {
+    r["curves"].as_array().map(|a| a.iter().filter_map(|x| x.as_str().map(str::to_string)).collect()).unwrap_or_default()
+}
+
+fn sk(s: &Session) -> solvecraft_sketch::Sketch {
+    s.model.state().sketch(s.active_sketch.unwrap()).unwrap().sketch.clone()
+}
+
+fn solved(s: &Session) -> bool {
+    s.model.state().sketch(s.active_sketch.unwrap()).unwrap().report.ok()
+}
+
+fn area(s: &Session) -> f64 {
+    s.model.state().sketch(s.active_sketch.unwrap()).unwrap().profiles.iter().map(|p| p.area).sum()
+}
+
+#[test]
+fn fillet_and_chamfer_corners() {
+    use std::f64::consts::PI;
+    // A constrained 40 × 20 rectangle: a fillet r5 on one corner keeps it solved and closed,
+    // with the area of the corner taken off.
+    let mut s = new_sketch();
+    let r = run(&mut s, "sketch.rectangle.two_point", json!({"p0": [0, 0], "p1": [40, 20]}));
+    let c = curves(&r);
+    let a0 = area(&s);
+    run(&mut s, "sketch.fillet", json!({"a": c[0], "b": c[1], "radius": 5}));
+    assert!(solved(&s));
+    assert!((area(&s) - (a0 - (25.0 - PI * 25.0 / 4.0))).abs() < 1e-6, "{}", area(&s));
+    // Several corners at once: the rest of the rectangle's corners.
+    let pts: Vec<String> = {
+        let k = sk(&s);
+        let li = |id: &str| k.curve_index(id).unwrap();
+        [(1, 2), (2, 3), (3, 0)]
+            .iter()
+            .map(|(x, y)| {
+                let (cx, cy) = (&k.curves[li(&c[*x])].kind, &k.curves[li(&c[*y])].kind);
+                let shared = cx.point_ids().into_iter().find(|p| cy.point_ids().contains(p)).unwrap();
+                k.points[shared].id.clone()
+            })
+            .collect()
+    };
+    run(&mut s, "sketch.fillet", json!({"points": pts, "radius": 5}));
+    assert!(solved(&s));
+    assert!((area(&s) - (a0 - 4.0 * (25.0 - PI * 25.0 / 4.0))).abs() < 1e-6, "{}", area(&s));
+    // Too large for a corner: a clear error, nothing changed.
+    let mut s = new_sketch();
+    let r = run(&mut s, "sketch.rectangle.two_point", json!({"p0": [0, 0], "p1": [40, 20]}));
+    let c = curves(&r);
+    let n = sk(&s).curves.len();
+    let e = s.execute("sketch.fillet", &json!({"a": c[0], "b": c[1], "radius": 30})).unwrap_err().to_string();
+    assert!(e.contains("too large") || e.contains("does not fit"), "{e}");
+    assert_eq!(sk(&s).curves.len(), n);
+    let e = s.execute("sketch.chamfer.equal_distance", &json!({"a": c[0], "b": c[1], "distance": 25})).unwrap_err().to_string();
+    assert!(e.contains("too large") || e.contains("does not fit") || e.contains("longer"), "{e}");
+    assert_eq!(sk(&s).curves.len(), n);
+    // A line meeting an arc, and two arcs (a slot's end rounded into a line).
+    let mut s = new_sketch();
+    let l = curves(&run(&mut s, "sketch.line", json!({"points": [[-20, 10], [0, 10]]})))[0].clone();
+    let a = curves(&run(&mut s, "sketch.arc.three_point", json!({"start": format!("{l}.end"), "end": [10, 0], "through": [7.0710678, 7.0710678]})))
+        [0]
+    .clone();
+    run(&mut s, "sketch.fillet", json!({"a": l, "b": a, "radius": 2}));
+    assert!(solved(&s));
+    let mut s = new_sketch();
+    let a1 = curves(&run(&mut s, "sketch.arc.three_point", json!({"start": [-10, 0], "end": [0, 0], "through": [-5, -5]})))[0].clone();
+    let a2 = curves(&run(&mut s, "sketch.arc.three_point", json!({"start": format!("{a1}.end"), "end": [10, 0], "through": [5, 2]})))[0].clone();
+    run(&mut s, "sketch.fillet", json!({"a": a1, "b": a2, "radius": 1}));
+    assert!(solved(&s));
+    // Chamfers keep a closed profile.
+    let mut s = new_sketch();
+    let r = run(&mut s, "sketch.rectangle.two_point", json!({"p0": [0, 0], "p1": [40, 20]}));
+    let c = curves(&r);
+    let a0 = area(&s);
+    run(&mut s, "sketch.chamfer.equal_distance", json!({"a": c[0], "b": c[1], "distance": 4}));
+    assert!(solved(&s));
+    assert!((area(&s) - (a0 - 8.0)).abs() < 1e-6, "{}", area(&s));
+}
diff --git a/crates/engine/src/cmd/sketch_modify.rs b/crates/engine/src/cmd/sketch_modify.rs
index d5d860ee..76c710e2 100644
--- a/crates/engine/src/cmd/sketch_modify.rs
+++ b/crates/engine/src/cmd/sketch_modify.rs
@@ -17,7 +17,7 @@ pub static COMMANDS: &[CommandSpec] = &[
         .at("SKETCH", "MODIFY")
         .icon("sketch_fillet")
         .enabled(in_sketch)
-        .params("point: corner shared by two curves (\"l1.end\") | a, b: two lines or arcs meeting at a corner; radius: expr"),
+        .params("point: corner shared by two curves (\"l1.end\") | points: [corners] (all rounded alike: one radius, the rest equal) | a, b: two lines or arcs meeting at a corner; radius: expr"),
     CommandSpec::new("sketch.chamfer.equal_distance", "Equal Distance Chamfer", chamfer_equal)
         .at("SKETCH", "MODIFY")
         .icon("sketch_chamfer")
@@ -480,48 +480,67 @@ fn cut_corner(sk: &mut Sketch, la: usize, lb: usize, c: usize, fa: usize, fb: us
 fn fillet(s: &mut Session, p: &Value) -> Result<Value> {
     let cmd = "sketch.fillet";
     let r_expr = expr(p, "radius").ok_or_else(|| bad(cmd, "`radius` must be a number or an expression"))?;
+    // Several corners at once (`points`), each like a single `point`.
+    let corners: Vec<Value> = match p.get("points").and_then(Value::as_array) {
+        Some(a) if !a.is_empty() && a.len() <= 500 => a.iter().map(|q| json!({ "point": q })).collect(),
+        Some(_) => return Err(bad(cmd, "`points` must list 1…500 corners")),
+        None => vec![p.clone()],
+    };
     let (out, info) = edit(s, p, cmd, false, |sk, doc| {
         let r = doc.eval(&r_expr, solvecraft_doc::expr::Kind::Length).map_err(|e| bad(cmd, format!("radius: {e}")))?;
         if !(r > 1e-9 && r < 1e8) {
             return Err(bad(cmd, "radius must be positive"));
         }
-        let (la, lb, c, fa, fb) = match corner(sk, p, cmd) {
-            Ok(x) => x,
-            // Not two lines: a corner with an arc.
-            Err(e) => {
-                let Some((arc, cons)) = round_corner(sk, p, r, cmd)? else { return Err(e) };
-                let mut cons = cons;
-                let pname = doc.new_model_param(&r_expr, "mm");
-                cons.push(sk.add_constraint(ConstraintKind::Radius { c: arc, value: r }, Some(pname.clone()))?);
-                return Ok((ids_of(sk, &[arc]), cons, pname));
-            }
-        };
-        let (pc, pa, pb) = (sk.point(c).unwrap_or_default(), sk.point(fa).unwrap_or_default(), sk.point(fb).unwrap_or_default());
-        let u = (pa - pc).normalized().ok_or_else(|| bad(cmd, "degenerate line"))?;
-        let v = (pb - pc).normalized().ok_or_else(|| bad(cmd, "degenerate line"))?;
-        let half = 0.5 * u.cross(v).atan2(u.dot(v)).abs();
-        if half < 1e-6 || half > std::f64::consts::FRAC_PI_2 - 1e-9 {
-            return Err(bad(cmd, "the lines are parallel"));
-        }
-        let d = r / half.tan();
-        let bis = (u + v).normalized().ok_or_else(|| bad(cmd, "the lines are parallel"))?;
-        let center = pc + bis * (r / half.sin());
-        let (ta, tb, _) = cut_corner(sk, la, lb, c, fa, fb, d, d, cmd)?;
-        let (qa, qb) = (sk.point(ta).unwrap_or_default(), sk.point(tb).unwrap_or_default());
-        let ccw = (qa - center).cross(qb - center) > 0.0;
-        let arc = if ccw {
-            sk.add_arc(center, qa, qb, [None, Some(ta), Some(tb)], None)?
-        } else {
-            sk.add_arc(center, qb, qa, [None, Some(tb), Some(ta)], None)?
-        };
-        let mut cons = vec![add_c(sk, ConstraintKind::Tangent { a: la, b: arc })?, add_c(sk, ConstraintKind::Tangent { a: lb, b: arc })?];
         let pname = doc.new_model_param(&r_expr, "mm");
-        cons.push(sk.add_constraint(ConstraintKind::Radius { c: arc, value: r }, Some(pname.clone()))?);
-        Ok((ids_of(sk, &[arc]), cons, pname))
+        let (mut arcs, mut cons) = (Vec::new(), Vec::new());
+        for q in &corners {
+            let (arc, mut c) = fillet_corner(sk, q, r, cmd)?;
+            // One radius for them all: the first carries the dimension, the rest are equal to it.
+            match arcs.first() {
+                None => c.push(sk.add_constraint(ConstraintKind::Radius { c: arc, value: r }, Some(pname.clone()))?),
+                Some(first) => c.push(add_c(sk, ConstraintKind::Equal { a: *first, b: arc })?),
+            }
+            cons.extend(c);
+            arcs.push(arc);
+        }
+        Ok((ids_of(sk, &arcs), cons, pname))
     })?;
     Ok(json!({"curves": out.0, "constraints": out.1, "param": out.2, "sketch": info}))
 }
 
+/// Round one corner (`point` or `a`, `b`) with an arc of radius `r` tangent to both curves:
+/// the arc and the tangent constraints.
+fn fillet_corner(sk: &mut Sketch, p: &Value, r: f64, cmd: &str) -> Result<(usize, Vec<String>)> {
+    let (la, lb, c, fa, fb) = match corner(sk, p, cmd) {
+        Ok(x) => x,
+        // Not two lines: a corner with an arc.
+        Err(e) => return round_corner(sk, p, r, cmd)?.ok_or(e),
+    };
+    let (pc, pa, pb) = (sk.point(c).unwrap_or_default(), sk.point(fa).unwrap_or_default(), sk.point(fb).unwrap_or_default());
+    let u = (pa - pc).normalized().ok_or_else(|| bad(cmd, "degenerate line"))?;
+    let v = (pb - pc).normalized().ok_or_else(|| bad(cmd, "degenerate line"))?;
+    let half = 0.5 * u.cross(v).atan2(u.dot(v)).abs();
+    if half < 1e-6 || half > std::f64::consts::FRAC_PI_2 - 1e-9 {
+        return Err(bad(cmd, "the lines are parallel"));
+    }
+    let d = r / half.tan();
+    if d >= pa.dist(pc) - 1e-9 || d >= pb.dist(pc) - 1e-9 {
+        return Err(bad(cmd, format!("the radius is too large for that corner (it needs {d:.3} mm of each line)")));
+    }
+    let bis = (u + v).normalized().ok_or_else(|| bad(cmd, "the lines are parallel"))?;
+    let center = pc + bis * (r / half.sin());
+    let (ta, tb, _) = cut_corner(sk, la, lb, c, fa, fb, d, d, cmd)?;
+    let (qa, qb) = (sk.point(ta).unwrap_or_default(), sk.point(tb).unwrap_or_default());
+    let ccw = (qa - center).cross(qb - center) > 0.0;
+    let arc = if ccw {
+        sk.add_arc(center, qa, qb, [None, Some(ta), Some(tb)], None)?
+    } else {
+        sk.add_arc(center, qb, qa, [None, Some(tb), Some(ta)], None)?
+    };
+    let cons = vec![add_c(sk, ConstraintKind::Tangent { a: la, b: arc })?, add_c(sk, ConstraintKind::Tangent { a: lb, b: arc })?];
+    Ok((arc, cons))
+}
+
 /// Fillet a corner where a line meets an arc, or two arcs meet: the arc of radius `r` touching
 /// both, nearest the corner; both curves are cut back to it. None when the corner is not of
 /// that kind.
@@ -1167,3 +1186,7 @@ mod tests;
 #[cfg(test)]
 #[path = "sketch_robust_tests.rs"]
 mod robust_tests;
+
+#[cfg(test)]
+#[path = "sketch_corner_tests.rs"]
+mod corner_tests;