**2.5. Cross-Check of the Cepheid Distances**

**2.5.1. Tests with Geometric Methods**

NGC4258 (M106) is a Seyfert 2 galaxy with
H_{2}O maser emission from
clouds orbiting around a black hole of mass 4 x 10^{7}
*M*_{}
located at the centre.
Precise VLBA measurements of Doppler velocities show that the motion
of the clouds is very close to Keplerian and is perturbed very little
(Miyoshi et
al. 1995).
A complete
determination is made for the orbital parameters including
centripetal acceleration and a bulk proper motion of the emission system.
This yields a geometric distance to NGC4258 to be 7.2 ± 0.3 Mpc
(Herrnstein et
al. 1999).

Maoz et al. (1999)
measured the distance to NGC4258 using the conventional
Cepheid PL relation, and
gave 8.1 ± 0.4 Mpc with (*m - M*)_{LMC} = 18.5. This
distance is 13% longer than that from the maser measurement.
The short LMC distance would bring the Cepheid distance in a
perfect agreement with the geometric distance.
This is, however, only one example,
and it can merely be a statistical effect: the deviation is only
twice the error, so it may happen with a chance probability of 5%.