diff --git a/NEWS.md b/NEWS.md
index c081684514..65a3d00ca2 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -46,6 +46,7 @@ xxxx-xx-xx
   - GEOSBuffer: Fix crash with Inf coordinates (GH-822, Dan Baston)
   - GEOSSTRtree_iterate: Do not return removed items (GH-833, Dan Baston)
   - IndexedFacetDistance: Fix crash with Inf coordinates (GH-821, Dan Baston)
+  - HausdorffDistance: Fix crash on collection containing empty point (GH-840, Dan Baston)
 
 
 ## Changes in 3.11.0
diff --git a/src/algorithm/distance/DistanceToPoint.cpp b/src/algorithm/distance/DistanceToPoint.cpp
index c80a8daf73..1891b63f83 100644
--- a/src/algorithm/distance/DistanceToPoint.cpp
+++ b/src/algorithm/distance/DistanceToPoint.cpp
@@ -40,6 +40,11 @@ DistanceToPoint::computeDistance(const geom::Geometry& geom,
                                  const geom::CoordinateXY& pt,
                                  PointPairDistance& ptDist)
 {
+    if (geom.isEmpty()) {
+        ptDist.initialize();
+        return;
+    }
+
     if(geom.getGeometryTypeId() == GEOS_LINESTRING) {
         const LineString* ls = static_cast<const LineString*>(&geom);
         computeDistance(*ls, pt, ptDist);
diff --git a/tests/unit/algorithm/distance/DiscreteHausdorffDistanceTest.cpp b/tests/unit/algorithm/distance/DiscreteHausdorffDistanceTest.cpp
index 0fb063ef85..188cd35e9c 100644
--- a/tests/unit/algorithm/distance/DiscreteHausdorffDistanceTest.cpp
+++ b/tests/unit/algorithm/distance/DiscreteHausdorffDistanceTest.cpp
@@ -201,5 +201,20 @@ void object::test<6>
     ensure("FE_INVALID raised", !std::fetestexcept(FE_INVALID));
 }
 
+// Crash on collection with empty components
+// https://github.com/libgeos/geos/issues/840
+template<>
+template<>
+void object::test<7>
+()
+{
+    auto g1 = reader.read("GEOMETRYCOLLECTION (POINT EMPTY, LINESTRING (0 0, 1 1))");
+    auto g2 = reader.read("POINT (1 2)");
+    auto g3 = reader.read("LINESTRING (0 0, 1 1)");
+
+    ensure_equals(DiscreteHausdorffDistance::distance(*g1, *g2),
+                  DiscreteHausdorffDistance::distance(*g2, *g3));
+}
+
 } // namespace tut