diff --git a/crates/engine/src/cmd/draw.rs b/crates/engine/src/cmd/draw.rs
index b073cf14..cf1998bf 100644
--- a/crates/engine/src/cmd/draw.rs
+++ b/crates/engine/src/cmd/draw.rs
@@ -937,11 +937,17 @@ impl Interactive for PolygonM {
                 s.last_used.polygon_circumscribed = !ins;
             }
             (Some(c), Some(ins), Input::Point(p)) => {
+                if c.near(p, 1e-12) {
+                    return Err(crate::EngineError::Other("Value must be positive and nonzero.".into()));
+                }
                 s.add_entity(lwpoly(polygon_vertices(c, n, p, ins), true))?;
                 return Ok(Step::Done);
             }
             (Some(c), Some(ins), Input::Text(t)) => {
                 let r = number(&t).ok_or_else(|| crate::EngineError::Other("Requires numeric distance or point.".into()))?;
+                if !r.is_finite() || r <= 0.0 {
+                    return Err(crate::EngineError::Other("Value must be positive and nonzero.".into()));
+                }
                 let rp = polygon_typed_radius_point(c, n, r, ins);
                 s.add_entity(lwpoly(polygon_vertices(c, n, rp, ins), true))?;
                 return Ok(Step::Done);
diff --git a/crates/engine/tests/draw_prompts.rs b/crates/engine/tests/draw_prompts.rs
index 4535b1be..0de2b953 100644
--- a/crates/engine/tests/draw_prompts.rs
+++ b/crates/engine/tests/draw_prompts.rs
@@ -107,3 +107,19 @@ fn circle_center_prompt_rejects_garbage() {
     s.cmdline("0,0 5").unwrap();
     assert!(matches!(last(&s), EntityKind::Circle(c) if (c.radius - 5.0).abs() < 1e-9));
 }
+
+#[test]
+fn polygon_radius_must_be_positive() {
+    for input in ["polygon 4 0,0 i 0", "polygon 4 0,0 c 0", "polygon 5 0,0 i -5", "polygon 5 0,0 c -5", "polygon 4 0,0 i 0,0", "polygon 4 0,0 c 0,0"]
+    {
+        let mut s = Session::new();
+        s.cmdline(input).unwrap();
+        assert_eq!(s.doc().unwrap().model.len(), 0, "{input}: no polygon");
+        assert!(logged(&s, "Value must be positive and nonzero."), "{input}: {:?}", s.log);
+        assert!(s.running.is_some(), "{input}: still at the radius prompt");
+        s.cmdline("2").unwrap();
+        assert!(s.running.is_none(), "{input}: a positive radius finishes");
+        assert_eq!(s.doc().unwrap().model.len(), 1, "{input}: one polygon");
+        assert!(matches!(last(&s), EntityKind::LwPolyline(p) if p.closed), "{input}");
+    }
+}