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Two circles of equal radius touch at the point P. One circle is fixed whilst the other moves, rolling without slipping, all the way round.
How many times does the moving coin revolve before returning to P?
What happens if the radius of the moving circle is half that of the fixed circle? Can you generalise your results further?
You may wish to use the GeoGebra interactivity below to test out your conjectures.
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.