Question 44
On a circular billiard table, a ball is reflected from a cushion as if it were being reflected from the tangent of the circle in the point of reflection.
A regular hexagon is drawn on a circular billiard table with its vertices on the circle.
A ball (in the form of a point) is placed on a side of the hexagon (not in one of the vertices). Determine a periodic path that the ball can take from this point with exactly four different points of reflection on the circle. In how many directions can the ball be brought onto such a path?
A regular hexagon is drawn on a circular billiard table with its vertices on the circle.
A ball (in the form of a point) is placed on a side of the hexagon (not in one of the vertices). Determine a periodic path that the ball can take from this point with exactly four different points of reflection on the circle. In how many directions can the ball be brought onto such a path?