diff --git a/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/Circular_arc_3.tex b/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/Circular_arc_3.tex
index 6de070e7af8..ef7456c7ddc 100644
--- a/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/Circular_arc_3.tex
+++ b/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/Circular_arc_3.tex
@@ -69,9 +69,10 @@ $y$-extremal point otherwise.
 
 \ccFunction{bool operator==(const Circular_arc_3<SphericalKernel> &a1,
 			const Circular_arc_3<SphericalKernel> &a2);}
-{Test for equality. Two arcs are equal, iff the centers and squared
+{Test for equality. Two arcs are equal, iff their non-oriented
+  supporting planes are equal, if the centers and squared
   radii of their respective supporting circles are equal, and if their
-  source and target are equal.} 
+  sources and targets are equal.} 
 
 \ccFunction{bool operator!=(const Circular_arc_3<SphericalKernel> &a1,
 			const Circular_arc_3<SphericalKernel> &a2);}
diff --git a/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/FunctorEqual.tex b/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/FunctorEqual.tex
index 6c3d1b92586..3106f13c9f6 100644
--- a/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/FunctorEqual.tex
+++ b/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/FunctorEqual.tex
@@ -20,12 +20,17 @@ An object \ccVar\ of this type must provide in addition:
 \ccMemberFunction{bool operator()
 	(const SphericalKernel::Circular_arc_3 &a0,
          const SphericalKernel::Circular_arc_3 &a1);}
-{For two arcs.}
+{For two arcs. Two arcs are equal, iff their non-oriented
+  supporting planes are equal, if the centers and squared
+  radii of their respective supporting circles are equal, and if their
+  sources and targets are equal.}
 
 \ccMemberFunction{bool operator()
 	(const SphericalKernel::Line_arc_3 &a0,
          const SphericalKernel::Line_arc_3 &a1);}
-{For two segments.}
+{For two segments. Two segments are equal, iff their non-oriented
+  supporting lines are equal (i.e. they define the same set of
+  points), and if their endpoints are the same.}
 
 \ccSeeAlso