  We consider a bar billiards problem for a triangle in the unit circle. For
the point on the unit circle, we construct a line from it in a counterclockwise
direction tangent to the triangle, and examine a map corresponding to the point
of intersection with the circle. We provide sufficient conditions for the
rotation number $\rho$ of this map to be $\frac{2}{5}$, as well as necessary
conditions for $\rho=\frac{2}{5}$.
