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...

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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)?

D.) Justify your answer to part C using multiple ways.

Mimi Yang, Created with GeoGebra