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?

*****

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?

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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.**View the archive of all weekly problems grouped by curriculum topic*

View the current weekly problem