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?
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?
Age
11 to 14
Challenge level
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 $(2,0)$.