Peri the winkle starts at the origin and slithers anticlockwise around a semicircle with centre $(4,0)$. Peri then slides anticlockwise around a second semicircle with centre $(6,0)$, and finally clockwise around a third semicircle with centre $(3,0)$.
Where does Peri end this expedition?
If you liked this problem, here is an NRICH task
that challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.