Peri the winkle

Weekly Problem 31 - 2014
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Peri the winkle starts at the origin $(0,0)$ and slithers anticlockwise around a semicircle with centre at $(4,0)$.

Peri then slides anticlockwise around a second semicircle with centre at $(6,0)$.

Finally, Peri slides clockwise around a third semicircle with centre at $(3,0)$.

Where does Peri end this expedition?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.