## Trigonometry of Rotating Circles!

In the following diagram, circle A has a radius of 8, and circle C has a radius of 7. The two circles are lined up vertically, and the shortest distance between them, EF, is 5 units. At time t = 0, the points B and D are placed maximally far apart on the circles. As time progresses, Point B rotates about A counterclockwise with the speed of 5 seconds per revolution, and Point D rotates about C with a speed of 6 seconds per revolution. As you can see, a red spring is tied between B and D. Sometimes it stretches, and other times it compresses...

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

A.) Right-click on the slider and un-check "Animation On", in order to toggle-control the t values yourself.

B.) What are the maximum and minimum lengths of this red spring as this system moves? (Hint: Might be easier if you place these circles in a coordinate system.)

C.) What is the period of the overall system (both circles included)?