As Clyde moves his broom around the circus ring, he thinks that he has finally found a job where he can make a clean sweep of things. Clyde is sweeping the ring where the lions perform in the Filbert Family Circus. The ring is 76 feet across and Clyde is using a broom 3 feet wide. He starts at the outside edge and works his way to the middle, making circles around the ring. After sweeping 3/4 of the ring, Clyde sees the lions coming with their trainer and scurries out of the ring. How many trips around the ring did he make?

If the ring is 76 feet across then the radius is 38 feet. Suppose that, when the lions come, Clyde has swept all except a circle of radius r as in the diagram.

The area of the entire ring is pi x 38² and the area of the unswept portion is pi x r². Since the swept portion is 3/4 of the ring, the area of the unswept portion is 1/4 of the ring. Thus

If you solve for r you should be able to answer the question.