In the Reflecting Ball Game a ball can be launched from points 1, 2, 3, 4, 5 or 6 in the direction shown. When a ball hits a side of rectangle it bounces at a angle back into the playing field. The path of the ball ends when it hits a corner point A, B, C or D. The path for starting point 5 is shown in the diagram. Each of the 15 non-overlapping squares of the playing field measures 2 cm by 2 cm. What is the length of the longest possible path for a ball launched from a starting point?
