  The nearly degenerate triplet bands with the $\pi g_{9/2}^{-1}\otimes \nu
h_{11/2} (g_{7/2},d_{5/2})$ configuration in $^{105}$Ag are studied via the
relativistic mean-field (RMF) theory and the multiparticle plus rotor model
(MPRM), which indicates that these bands are associated with chiral symmetry
and pseudospin symmetry. The configuration-fixed constrained triaxial RMF
calculations exhibit the pseudospin symmetry in single particle spectra and the
triaxial shape coexistence. The experimental excitation energies and the
electromagnetic transition probabilities for the triplet bands are reproduced
very well by the MPRM calculaitons. The chiral doublet bands show the same
phase in the $B(M1)/B(E2)$ staggering, while the pseudospin doublet bands hold
the opposite phase. The coexistence of chiral symmetry and pseudospin symmetry
in one nucleus and its corresponding characteristic of the rotational structure
are discussed for the first time.
