diff --git a/crates/ui-egui/src/inference.rs b/crates/ui-egui/src/inference.rs
new file mode 100644
index 00000000..cafb1d4a
--- /dev/null
+++ b/crates/ui-egui/src/inference.rs
@@ -0,0 +1,226 @@
+//! Drawing-time inference for the Line tool, like Fusion's: while the next point is placed the
+//! cursor snaps to directions and places taken from the existing geometry (parallel or
+//! perpendicular to a line, on the extension of a line, tangent to a circle or arc). A dashed
+//! guide and a label show it; placing the point adds the matching constraint.
+
+use std::cell::RefCell;
+
+use egui::{Shape, Stroke};
+use serde_json::json;
+use solvecraft_engine::geom::Vec2;
+use solvecraft_engine::sketch::{CurveKind, Sketch};
+
+use crate::SolveApp;
+use crate::theme::Tokens;
+use crate::viewport::Proj;
+
+#[derive(Clone, Debug, PartialEq)]
+pub enum Kind {
+    Parallel,
+    Perpendicular,
+    Extension,
+    Tangent,
+}
+
+/// A snap taken from existing geometry: what, to which curve, where the point goes, how far the
+/// cursor was moved, and the guide to draw (sketch coordinates).
+#[derive(Clone, Debug, PartialEq)]
+pub struct Inference {
+    pub kind: Kind,
+    pub curve: String,
+    pub at: Vec2,
+    pub dist: f64,
+    pub guide: (Vec2, Vec2),
+}
+
+impl Inference {
+    pub fn label(&self) -> &'static str {
+        match self.kind {
+            Kind::Parallel => "//",
+            Kind::Perpendicular => "\u{22a5}",
+            Kind::Extension => "Ext",
+            Kind::Tangent => "T",
+        }
+    }
+}
+
+thread_local! {
+    static PENDING: RefCell<Option<Inference>> = const { RefCell::new(None) };
+}
+
+/// Forget the current inference (another snap won, or the tool ended).
+pub fn clear() {
+    PENDING.with(|p| *p.borrow_mut() = None);
+}
+
+pub fn current() -> Option<Inference> {
+    PENDING.with(|p| p.borrow().clone())
+}
+
+fn keep(i: Option<Inference>) -> Option<Inference> {
+    PENDING.with(|p| *p.borrow_mut() = i.clone());
+    i
+}
+
+fn line_ends(sk: &Sketch, c: usize) -> Option<(Vec2, Vec2)> {
+    match sk.curves.get(c)?.kind {
+        CurveKind::Line { a, b } => Some((sk.point(a)?, sk.point(b)?)),
+        _ => None,
+    }
+}
+
+/// Tangent from the previous point `prev` to a circle or arc, when the cursor `lp` is near the
+/// tangent point (within `tol`).
+pub fn tangent(sk: &Sketch, prev: Vec2, lp: Vec2, tol: f64) -> Option<Inference> {
+    let mut best: Option<Inference> = None;
+    for (i, c) in sk.curves.iter().enumerate() {
+        if c.construction || !matches!(c.kind, CurveKind::Circle { .. } | CurveKind::Arc { .. }) {
+            continue;
+        }
+        let (Some(o), Some(r)) = (sk.center(i), sk.radius(i)) else { continue };
+        let d = prev.dist(o);
+        if d <= r + 1e-9 {
+            continue;
+        }
+        // The two tangent points seen from `prev`.
+        let base = (prev - o).angle();
+        let half = (r / d).acos();
+        for s in [-1.0, 1.0] {
+            let t = o + Vec2::from_angle(base + s * half) * r;
+            let on_arc = sk.shape(i).is_none_or(|sh| sh.dist(t) < 1e-6);
+            let e = t.dist(lp);
+            if on_arc && e < tol && best.as_ref().is_none_or(|b| e < b.dist) {
+                best = Some(Inference { kind: Kind::Tangent, curve: c.id.clone(), at: t, dist: e, guide: (prev, t) });
+            }
+        }
+    }
+    keep(best)
+}
+
+/// Directions and places from lines: parallel or perpendicular to a line (from `prev`), or on
+/// the extension of a line beyond its ends.
+pub fn lines(sk: &Sketch, prev: Vec2, lp: Vec2, tol: f64) -> Option<Inference> {
+    let mut best: Option<Inference> = None;
+    let mut offer = |i: Inference| {
+        if best.as_ref().is_none_or(|b| i.dist < b.dist) {
+            best = Some(i);
+        }
+    };
+    let v = lp - prev;
+    if v.len() < tol * 2.0 {
+        return keep(None);
+    }
+    for (i, c) in sk.curves.iter().enumerate() {
+        if c.construction && c.link.is_none() {
+            continue;
+        }
+        let Some((a, b)) = line_ends(sk, i) else { continue };
+        let Some(dir) = (b - a).normalized() else { continue };
+        // Axis-aligned directions are the H/V snaps' business.
+        let axis = dir.x.abs() < 1e-9 || dir.y.abs() < 1e-9;
+        let touches = a.dist(prev) < 1e-9 || b.dist(prev) < 1e-9;
+        for (kind, d) in [(Kind::Parallel, dir), (Kind::Perpendicular, dir.perp())] {
+            if axis || (kind == Kind::Parallel && touches) {
+                continue;
+            }
+            let t = v.dot(d);
+            let at = prev + d * t;
+            let e = at.dist(lp);
+            if e < tol {
+                offer(Inference {
+                    kind,
+                    curve: c.id.clone(),
+                    at,
+                    dist: e,
+                    guide: (prev - d * (t.signum() * tol * 6.0), at + d * (t.signum() * tol * 6.0)),
+                });
+            }
+        }
+        // The extension: beyond the ends, on the line's own (infinite) line.
+        let s = (lp - a).dot(dir);
+        let len = a.dist(b);
+        if !(-tol..=len + tol).contains(&s) {
+            let at = a + dir * s;
+            let e = at.dist(lp);
+            if e < tol * 0.8 && !touches {
+                let from = if s < 0.0 { a } else { b };
+                offer(Inference { kind: Kind::Extension, curve: c.id.clone(), at, dist: e * 0.9, guide: (from, at) });
+            }
+        }
+    }
+    keep(best)
+}
+
+/// The Line tool placed a segment ending at `end` (the new line `line`): add the constraint of
+/// the inference it was snapped by.
+pub fn commit(app: &mut SolveApp, line: &str, end: Vec2) {
+    let Some(i) = current().filter(|i| i.at.dist(end) < 1e-9) else { return };
+    clear();
+    let (cmd, params) = match i.kind {
+        Kind::Parallel => ("ConstraintParallel", json!({"a": i.curve, "b": line})),
+        Kind::Perpendicular => ("ConstraintPerpendicular", json!({"a": i.curve, "b": line})),
+        Kind::Tangent => ("ConstraintTangent", json!({"a": i.curve, "b": line})),
+        Kind::Extension => ("ConstraintCoincident", json!({"a": format!("{line}.end"), "b": i.curve})),
+    };
+    // An inference that would over-constrain the sketch is simply not kept.
+    let _ = app.session.execute(cmd, &params);
+}
+
+/// The dashed guide of the current inference (its label is the snap hint) (while the Line tool is active).
+pub fn show(app: &SolveApp, painter: &egui::Painter, proj: &Proj) {
+    if app.tool.as_ref().is_none_or(|t| t.cmd != "DrawPolyline") {
+        return;
+    }
+    let Some(i) = current() else { return };
+    let st = app.session.model.state();
+    let Some(ss) = app.session.active_sketch.and_then(|s| st.sketch(s)) else { return };
+    let to = |p: Vec2| proj.to_screen(ss.plane.to_world(p));
+    let tk = Tokens::get();
+    if let (Some(a), Some(b)) = (to(i.guide.0), to(i.guide.1)) {
+        painter.add(Shape::dashed_line(&[a, b], Stroke::new(1.0, tk.rubber_band), 5.0, 4.0));
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn sk() -> Sketch {
+        let mut s = Sketch::new();
+        let _ = s.add_line(Vec2::new(0.0, 0.0), Vec2::new(10.0, 10.0), None, None, Some("l1"));
+        let _ = s.add_circle(Vec2::new(30.0, 0.0), 5.0, None, Some("c1"));
+        s
+    }
+
+    #[test]
+    fn parallel_and_perpendicular_from_the_previous_point() {
+        let s = sk();
+        let i = lines(&s, Vec2::new(0.0, 20.0), Vec2::new(10.2, 29.9), 0.5).expect("parallel");
+        assert_eq!(i.kind, Kind::Parallel);
+        assert!((i.at - Vec2::new(0.0, 20.0)).cross(Vec2::new(1.0, 1.0)).abs() < 1e-9);
+        let i = lines(&s, Vec2::new(0.0, 20.0), Vec2::new(10.1, 10.0), 0.5).expect("perpendicular");
+        assert_eq!(i.kind, Kind::Perpendicular);
+        assert!(lines(&s, Vec2::new(0.0, 20.0), Vec2::new(10.0, 25.0), 0.5).is_none());
+    }
+
+    #[test]
+    fn extension_beyond_the_end() {
+        let s = sk();
+        let i = lines(&s, Vec2::new(30.0, 15.0), Vec2::new(20.1, 19.9), 0.5).expect("extension");
+        assert_eq!(i.kind, Kind::Extension);
+        assert!((i.at.x - i.at.y).abs() < 1e-9 && i.at.x > 10.0);
+    }
+
+    #[test]
+    fn tangent_point_on_a_circle() {
+        let s = sk();
+        let prev = Vec2::new(30.0, 20.0);
+        // Tangent points from (30, 20) to the circle at (30, 0) r 5.
+        let half = (5.0f64 / 20.0).acos();
+        let t = Vec2::new(30.0, 0.0) + Vec2::from_angle(std::f64::consts::FRAC_PI_2 + half) * 5.0;
+        let i = tangent(&s, prev, t + Vec2::new(0.2, 0.1), 0.5).expect("tangent");
+        assert_eq!(i.kind, Kind::Tangent);
+        assert!(i.at.dist(t) < 1e-9);
+        assert!((i.at - Vec2::new(30.0, 0.0)).dot(i.at - prev).abs() < 1e-9);
+    }
+}
diff --git a/crates/ui-egui/src/lib.rs b/crates/ui-egui/src/lib.rs
index b43e5fb8..1599edf6 100644
--- a/crates/ui-egui/src/lib.rs
+++ b/crates/ui-egui/src/lib.rs
@@ -20,6 +20,7 @@ pub mod dialogs_sheet;
 pub mod dim_view;
 pub mod gpu;
 pub mod icons;
+pub mod inference;
 #[cfg(test)]
 mod menu_tests;
 pub mod palette;
diff --git a/crates/ui-egui/src/sketch_tools.rs b/crates/ui-egui/src/sketch_tools.rs
index 7dbd02c3..58039fe0 100644
--- a/crates/ui-egui/src/sketch_tools.rs
+++ b/crates/ui-egui/src/sketch_tools.rs
@@ -75,6 +75,7 @@ pub fn refine_snap(
     plane: &solvecraft_engine::geom::Plane,
     lp: Vec2,
 ) -> Option<(Vec2, Option<String>)> {
+    crate::inference::clear();
     // Millimetres per pixel here.
     let (a, b) = (proj.to_screen(plane.to_world(lp))?, proj.to_screen(plane.to_world(lp + Vec2::X))?);
     let px = 1.0 / (a.distance(b) as f64).max(1e-9);
@@ -110,6 +111,15 @@ pub fn refine_snap(
         }
         None => PREV.with(Cell::get),
     };
+    // Line tool: the tangent point of a circle or arc (before plain "on the curve").
+    let line_tool = app.tool.as_ref().is_none_or(|t| t.cmd == "DrawPolyline");
+    if best.is_none()
+        && line_tool
+        && let Some(prev) = prev
+        && let Some(i) = crate::inference::tangent(sk, prev, lp, tol)
+    {
+        best = Some((i.dist, i.label(), i.at));
+    }
     // On a curve (coincident with it).
     if best.is_none() {
         for (i, c) in sk.curves.iter().enumerate() {
@@ -135,6 +145,14 @@ pub fn refine_snap(
             best = Some((dx, "V", Vec2::new(prev.x, g(lp.y))));
         }
     }
+    // Line tool: parallel or perpendicular to a line, or on a line's extension.
+    if best.is_none()
+        && line_tool
+        && let Some(prev) = prev
+        && let Some(i) = crate::inference::lines(sk, prev, lp, tol)
+    {
+        best = Some((i.dist, i.label(), i.at));
+    }
     SNAP.with(|s| *s.borrow_mut() = best.map(|(_, l, p)| (l, p)));
     // A midpoint snap is a point argument the commands understand ("mid:<line>").
     best.map(|(_, l, p)| {
diff --git a/crates/ui-egui/src/tools.rs b/crates/ui-egui/src/tools.rs
index b93ddaae..e706b0ae 100644
--- a/crates/ui-egui/src/tools.rs
+++ b/crates/ui-egui/src/tools.rs
@@ -190,6 +190,7 @@ pub fn place(app: &mut SolveApp, p: (Vec2, Option<String>)) {
                 dimension(app, &tool, &curves);
                 // Chain: the next segment starts at this one's end point.
                 if let Some(id) = curves.first() {
+                    crate::inference::commit(app, id, b.0);
                     let last = tool.pts.len() - 1;
                     tool.pts[last].1 = Some(format!("{id}.end"));
                 }
diff --git a/crates/ui-egui/src/viewport.rs b/crates/ui-egui/src/viewport.rs
index fa08898e..76f78130 100644
--- a/crates/ui-egui/src/viewport.rs
+++ b/crates/ui-egui/src/viewport.rs
@@ -1272,6 +1272,7 @@ pub fn show(app: &mut SolveApp, ui: &mut egui::Ui) {
     overlays(app, &painter, &proj);
     crate::dim_view::show(app, ui, &painter, &proj);
     crate::sketch3d::show(app, &painter, &proj);
+    crate::inference::show(app, &painter, &proj);
     hover_highlight(app, &painter, &proj);
     points_2d(app, &painter, &proj);
     if let Some(bx) = app.viewport.boxsel {