diff --git a/crates/geom/src/measure.rs b/crates/geom/src/measure.rs
index 03de47cd0..717ec9d69 100644
--- a/crates/geom/src/measure.rs
+++ b/crates/geom/src/measure.rs
@@ -8,11 +8,16 @@ pub const FLATTEN_TOL: f64 = 0.05;
 /// The most flattened points a path is measured with; longer paths are refused.
 pub const MAX_SAMPLES: usize = 40_000;
 
-/// Every coordinate is finite and of a sane magnitude: within [`crate::MAX_COORD`], the cap the
-/// shape builders hold their sizes, radii and angles to (inclusive, so a path built at the cap
-/// still measures).
+/// How far out a measured coordinate may lie. The shape builders hold their sizes, radii and
+/// angles to [`crate::MAX_COORD`], so a path built at the cap has its points there and the
+/// control points of its curves a little past them (the cubics approximating an arc reach past
+/// the arc's box by up to about a tenth of the radius). Half as much again keeps every built path
+/// measurable and still refuses the absurd.
+pub const MAX_MEASURED_COORD: f64 = crate::MAX_COORD * 1.5;
+
+/// Every coordinate is finite and of a sane magnitude (within [`MAX_MEASURED_COORD`]).
 pub fn finite_path(path: &BezPath) -> bool {
-    let ok = |p: &Point| p.x.is_finite() && p.y.is_finite() && p.x.abs() <= crate::MAX_COORD && p.y.abs() <= crate::MAX_COORD;
+    let ok = |p: &Point| p.x.is_finite() && p.y.is_finite() && p.x.abs() <= MAX_MEASURED_COORD && p.y.abs() <= MAX_MEASURED_COORD;
     path.elements().iter().all(|el| match el {
         PathEl::MoveTo(p) | PathEl::LineTo(p) => ok(p),
         PathEl::QuadTo(a, b) => ok(a) && ok(b),
diff --git a/crates/geom/src/tests.rs b/crates/geom/src/tests.rs
index 3e9fdce1e..24f47e1c5 100644
--- a/crates/geom/src/tests.rs
+++ b/crates/geom/src/tests.rs
@@ -68,11 +68,25 @@ fn paths_at_the_cap_still_measure() {
     line.move_to(Point::new(-MAX_COORD, 0.0));
     line.line_to(Point::new(MAX_COORD, -MAX_COORD));
     assert!(polylines(&line).is_some(), "a line between the cap's corners measures");
+    // A curve at the cap: the cubics approximating the arc have control points past the cap, and
+    // the path still measures.
+    let arc = ellipse(MAX_COORD, 1.0, -0.15, 0.2, 0.0);
+    let reach = arc
+        .elements()
+        .iter()
+        .flat_map(|el| match el {
+            kurbo::PathEl::CurveTo(a, b, _) => vec![a.x, b.x],
+            _ => vec![],
+        })
+        .fold(0.0, f64::max);
+    assert!(reach > MAX_COORD, "a control point lies past the cap: {reach}");
+    assert!(finite_path(&arc));
+    assert!(polylines(&arc).is_some(), "an arc at the cap measures");
     let mut past = BezPath::new();
     past.move_to(Point::new(0.0, 0.0));
-    past.line_to(Point::new(MAX_COORD + 1.0, 0.0));
+    past.line_to(Point::new(2.0 * MAX_COORD, 0.0));
     assert!(!finite_path(&past));
-    assert!(polylines(&past).is_none(), "a coordinate past the cap is refused");
+    assert!(polylines(&past).is_none(), "a coordinate well past the cap is refused");
 }
 
 #[test]