Turning Triangles
A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle. How does the answer change if the triangle is a right-angled triangle or an equilateral triangle?
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Roundabout
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square.
Describe the locus of the centre of the circle and its length.
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Is There a Theorem?
Draw a square. (This square will be fixed, think of it as being glued to the page.) 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?
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Rollin' Rollin' Rollin;
Two circles of equal radius kiss 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?
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