Two chords ^@AB^@ and ^@CD^@ of length ^@ 4 \space cm ^@, and ^@ 5 \space cm ^@ respectively of a circle are parallel to each other and are on the opposite sides of its center. If the distance between ^@AB^@ and ^@CD^@ is ^@ 3 \space cm,^@ find the approximate radius of the circle.
Lien and Lian each have a bag that contains one ball each of the colors blue, white, yellow, grey and pink. Lien randomly selects a ball from her bag and puts it in Lian's bag. Then Lian randomly selects a ball from her bag and puts it in Lien's bag. What is the probability that after this the contents of the bag are the same as before?
There is a rectangle ABCD, with sides AB = CD = 27, and sides and BC = DA = 36. The rectangle is rotated 90° clockwise about C, then rotated 90°clockwise about the new location of the point that D after the first rotation. What is the length of the path traveled by point A?