diff --git a/src/Mod/Part/App/Attacher.cpp b/src/Mod/Part/App/Attacher.cpp
index 9fe2c114a1..f5f5beffae 100644
--- a/src/Mod/Part/App/Attacher.cpp
+++ b/src/Mod/Part/App/Attacher.cpp
@@ -1377,7 +1377,7 @@ AttachEngine3D::_calculateAttachedPlacement(const std::vector<App::DocumentObjec
                 else {
                     TopLoc_Location loc;
                     Handle(Geom_Surface) surf = BRep_Tool::Surface(face, loc);
-                    GeomLib_IsPlanarSurface check(surf);
+                    GeomLib_IsPlanarSurface check(surf, precision);
                     if (check.IsPlanar()) {
                         plane = check.Plan();
                     }
@@ -2095,11 +2095,17 @@ Base::Placement AttachEnginePlane::_calculateAttachedPlacement(
     //reuse Attacher3d
     Base::Placement plm;
     AttachEngine3D attacher3D;
+    attacher3D.precision = precision;
     attacher3D.setUp(*this);
     plm = attacher3D._calculateAttachedPlacement(objs,subs,origPlacement);
     return plm;
 }
 
+double AttachEnginePlane::planarPrecision()
+{
+    return 2.0e-7;  // NOLINT
+}
+
 //=================================================================================
 
 TYPESYSTEM_SOURCE(Attacher::AttachEngineLine, Attacher::AttachEngine)
diff --git a/src/Mod/Part/App/Attacher.h b/src/Mod/Part/App/Attacher.h
index a990069f0b..206719c27d 100644
--- a/src/Mod/Part/App/Attacher.h
+++ b/src/Mod/Part/App/Attacher.h
@@ -391,6 +391,7 @@ public: //members
     bool mapReverse = false;
     double attachParameter = 0.0;
     double surfU = 0.0, surfV = 0.0;
+    double precision = 1.0e-7;
     Base::Placement attachmentOffset;
 
     /**
@@ -489,6 +490,7 @@ public:
         const std::vector<App::DocumentObject*> &objs,
         const std::vector<std::string> &subs,
         const Base::Placement &origPlacement) const override;
+    static double planarPrecision();
 };
 
 //attacher specialized for datum lines
diff --git a/src/Mod/Part/App/Part2DObject.cpp b/src/Mod/Part/App/Part2DObject.cpp
index 0f363bbe0d..dd818c4227 100644
--- a/src/Mod/Part/App/Part2DObject.cpp
+++ b/src/Mod/Part/App/Part2DObject.cpp
@@ -60,7 +60,9 @@ PROPERTY_SOURCE_WITH_EXTENSIONS(Part::Part2DObject, Part::Feature)
 Part2DObject::Part2DObject()
 {
     AttachExtension::initExtension(this);
-    this->setAttacher(new Attacher::AttachEnginePlane);
+    auto engine = new Attacher::AttachEnginePlane;
+    engine->precision = Attacher::AttachEnginePlane::planarPrecision();
+    this->setAttacher(engine);
 }
 
 
diff --git a/src/Mod/PartDesign/Gui/SketchWorkflow.cpp b/src/Mod/PartDesign/Gui/SketchWorkflow.cpp
index 19ef91df16..3b10347b58 100644
--- a/src/Mod/PartDesign/Gui/SketchWorkflow.cpp
+++ b/src/Mod/PartDesign/Gui/SketchWorkflow.cpp
@@ -141,7 +141,7 @@ public:
             throw WrongSupportException();
         }
 
-        if (!subshape.isPlanar()) {
+        if (!subshape.isPlanar(Attacher::AttachEnginePlane::planarPrecision())) {
             throw SupportNotPlanarException();
         }
     }