Imagine a circle of diameter $1$ unit, and another circle of a
similar diameter, and another.

What is the total perimeter of these three circles (you can leave your answer with $\pi$ in it)?

What is the perimeter of a circle of diameter $3$ units?

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Now imagine two circles - one of diameter $2$ units and one of diameter $3$ units.

What is the total perimeter of these two circles?

What is the perimeter of a circle of diameter 5units?

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What do you notice?

Is this generally the case with combinations of circles whose total diameters are equal?

Can you explain why?

What is the total perimeter of these three circles (you can leave your answer with $\pi$ in it)?

What is the perimeter of a circle of diameter $3$ units?

*****

Now imagine two circles - one of diameter $2$ units and one of diameter $3$ units.

What is the total perimeter of these two circles?

What is the perimeter of a circle of diameter 5units?

*****

What do you notice?

Is this generally the case with combinations of circles whose total diameters are equal?

Can you explain why?

*This problem is taken from the UKMT Mathematical Challenges.*