### Triangle Inequality

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

### How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

### Speeding Up, Slowing Down

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

# Rollin' Rollin' Rollin'

##### Stage: 3 Challenge Level:

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?

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Here are two related problems you might like to take a look at:
Rolling Around
Is There a Theorem?