  To use galaxy clusters as a cosmological probe, it is important to account
for their triaxiality. Assuming that the triaxial shapes of galaxy clusters are
induced by the tidal interaction with the surrounding matter, Lee and Kang
recently developed a reconstruction algorithm for the measurement of the axial
ratio of a triaxial cluster. We examine the validity of this reconstruction
algorithm by performing an observational test of it with the Virgo cluster as a
target. We first modify the LK06 algorithm by incorporating the two dimensional
projection effect. Then, we analyze the 1275 member galaxies from the Virgo
Cluster Catalogue and find the projected direction of the Virgo cluster major
axis by measuring the anisotropy in the spatial distribution of the member
galaxies in the two dimensional projected plane. Applying the modified
reconstruction algorithm to the analyzed data, we find that the axial ratio of
the triaxial Virgo cluster is (1: 0.54 : 0.73). This result is consistent with
the recent observational report from the Virgo Cluster Survey, proving the
robustness of the reconstruction algorithm. It is also found that at the inner
radii the shape tends to be more like prolate. We discuss the possible effect
of the Virgo cluster triaxiality on the mass estimation.
