You may also like

problem icon

Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

problem icon

Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

problem icon

Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Weekly Problem 13 - 2006

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
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?

*****

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 previous week's solution
View the current weekly problem