diff --git a/lib/matplotlib/bezier.py b/lib/matplotlib/bezier.py
index f310f287e2c0..069e20d05916 100644
--- a/lib/matplotlib/bezier.py
+++ b/lib/matplotlib/bezier.py
@@ -171,9 +171,17 @@ def find_bezier_t_intersecting_with_closedpath(
 
         if start_inside ^ middle_inside:
             t1 = middle_t
+            if end == middle:
+                # Edge case where infinite loop is possible
+                # Caused by large numbers relative to tolerance
+                return t0, t1
             end = middle
         else:
             t0 = middle_t
+            if start == middle:
+                # Edge case where infinite loop is possible
+                # Caused by large numbers relative to tolerance
+                return t0, t1
             start = middle
             start_inside = middle_inside
 
diff --git a/lib/matplotlib/tests/test_bezier.py b/lib/matplotlib/tests/test_bezier.py
new file mode 100644
index 000000000000..65e2c616e738
--- /dev/null
+++ b/lib/matplotlib/tests/test_bezier.py
@@ -0,0 +1,17 @@
+"""
+Tests specific to the bezier module.
+"""
+
+from matplotlib.bezier import inside_circle, split_bezier_intersecting_with_closedpath
+
+
+def test_split_bezier_with_large_values():
+    # These numbers come from gh-27753
+    arrow_path = [(96950809781500.0, 804.7503795623779),
+                  (96950809781500.0, 859.6242585800646),
+                  (96950809781500.0, 914.4981375977513)]
+    in_f = inside_circle(96950809781500.0, 804.7503795623779, 0.06)
+    split_bezier_intersecting_with_closedpath(arrow_path, in_f)
+    # All we are testing is that this completes
+    # The failure case is an infinite loop resulting from floating point precision
+    # pytest will timeout if that occurs