  We discuss the Alexandrov-Toponogov comparison theorem under the conditions
of radial curvature of a pointed manifold (M,o) with reference surface of
revolution. There are two obstructions to make the comparison theorem for a
triangle one of whose vertices is a base point o. One is the cut points of
another vertex of a comparison triangle in the reference surface of revolution.
The other is the cut points of the base point o in M. We find a condition under
which the omparison theorem is valid for any geodesic triangle with a vertex at
o in M.
