A circular hoop and a rectangular frame are standing on the level ground as shown. The diagonal $$AB$$ is extended to meet the circular hoop at the highest point $$C$$. If $$AB = 18$$ cm, $$BC = 32$$ cm, the radius of the hoop (in cm) is ------.

TO BE FILLED - figure required. The exact tangency relationship between the rectangular frame and the circular hoop (which side of the frame touches the hoop, and where) cannot be determined with confidence from the extracted figure, and different reasonable assumptions give very different, non-matching radii.