diff --git a/masque/library.py b/masque/library.py
index 82277e1..90202dc 100644
--- a/masque/library.py
+++ b/masque/library.py
@@ -542,7 +542,7 @@ class ILibraryView(Mapping[str, 'Pattern'], metaclass=ABCMeta):
         Return:
             Topologically sorted list of pattern names.
         """
-        return list(TopologicalSorter(self.child_graph()).static_order())
+        return cast(list[str], list(TopologicalSorter(self.child_graph()).static_order()))
 
     def find_refs_local(
             self,
diff --git a/masque/shapes/arc.py b/masque/shapes/arc.py
index da5d3f8..67d932d 100644
--- a/masque/shapes/arc.py
+++ b/masque/shapes/arc.py
@@ -233,7 +233,7 @@ class Arc(Shape):
         r0, r1 = self.radii
 
         # Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation)
-        a_ranges = self._angles_to_parameters()
+        a_ranges = cast(tuple[tuple[float, float], tuple[float, float]], self._angles_to_parameters())
 
         # Approximate perimeter via numerical integration