Peri the Winkle
Age
11 to 14
Challenge level
Weekly Problem 31 - 2014
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?
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.
Student Solutions
Answer: $(2,0)$
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After traversing the first semicircle, Peri will be at the point $(8,0)$;
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After the second semicircle Peri will be at $(4,0)$
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After the third semicircle, Peri will be at the point $(2,0)$.