  In a very interesting paper, Hod has proven that the equatorial null circular
geodesic provides the extreme orbital period to circle a kerr black hole, which
is closely related to the Fermat's principle. In the present paper, we extend
the discussion to kerr black holes with scalar field hair. We show that the
circle with the extreme orbital period is still identical to the null circular
geodesic. Our analysis also implies that the Hod's theorem may be a general
property in any axially symmetric spacetime with reflection symmetry on the
equatorial plane.
