  The persistence of $\alpha+\alpha+t$ cluster configuration in the ground
state of $^{11}$B is discussed. The $\alpha$ particles emitted from excited
states of $^{12}$C could be utilized for cancer treatment, where the cluster
states are created by a clinical proton beam on the $^{11}$B target. Although
the cross section has been already available, for the nuclear structure side,
whether the ground state of $^{11}$B contains the seeds of the cluster states
is a crucial question, since the cluster structure may be washed out by the
spin-orbit interaction, which has been known as a driving force to break the
$\alpha$ clusters. For this purpose, in addition to the basis states with
cluster configurations, we include their breaking effects by employing the
antisymmetrized quasi cluster model (AQCM). The inclusion of the breaking
effect of $\alpha+\alpha+t$ cluster structure is found to contribute to the
lowering of the ground-state energy by about 2 MeV. Assuming the typical
three-$\alpha$ cluster state of $^{12}$C as an equilateral triangular
configuration with the relative distances of $\approx 4$ fm, the ground state
of $^{11}$B is found to have a certain squared overlap with such state when a
proton approaches. The third $3/2^{-}$ state has been suggested as a cluster
state both theoretically and experimentally, and we confirmed the
well-developed clustering.
