  We consider square and equilateral triangular open acoustic resonators with
the $C_{4v}$ and $C_{3v}$ symmetries, respectively. There is an unique property
of square and triangular resonators of accidental number four-fold degeneracy
of eigenstates that gives rise to two-fold degenerate Friedrich-Wintgen (FW)
BICs. Compared to usual FW BICs the degenerate FW BICs maintain high $Q$-factor
in wide range of the size of resonators. That removes the fabrication
difficulties of proper choice of resonator. The presence of degenerate BICs in
triangular resonators is extremely sensitive to switch output flows by small
perturbations with $100\%$ efficiency.
