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## 'Triangles and Petals' printed from http://nrich.maths.org/

Look at the equilateral
triangle rotating around the equilateral triangle. It produces a
flower with three petals:

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Can you work out the
perimeter of the flower's petals?

Now consider a flower made
by the triangle rotating about a square - what is the perimeter of
the petals now?

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What is the perimeter when
the centre of the flower is a regular pentagon, hexagon,
heptagon...?

What can you say about the increase in perimeter as the number of
sides of the centre shape increases?

Can you explain this increase?

What would be the perimeter of a flower whose centre is a regular
$100$-sided polygon with side length $r$?

It may help to work in terms of $\pi$
throughout this problem.