Carousel Puzzler

Topic:
Circle
This file contains three interactive constructions that illustrate some of the relationships in the Carousel Problem (from CarTalk http://www.cartalk.com/content/painting-carousel-0 ). One shows the pythagorean relationship between the radii of the three circles, one shows this relationship through triangle similarity, and the third shows a more general relationship between any two chords in a circle. Explore what happens to the area of the circle centered at B as the radius of the inner circle approaches that of the outer circle or approaches zero.
Use the interactive constructions to explore the relationship between the radii of the three circles: one shows this relationship through the pythagorean theorem, another triangle similarity, and the third shows a more general relationship between any two chords in a circle. Explore what happens to the area of the circle centered at B as the radius of the inner circle approaches that of the outer circle or approaches zero. In circle H, try to explain how you might prove that the triangles formed are always similar - How is the Intersecting Chord Theorem (if two chords on a circle intersect, the product of the lengths of the two segments of one chord equal the product of the lengths of the two segments of the other chord) a consequence of the similarity relationship?