IMC 2012 Q18
18. 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?
- A (0, 0)
- B (1, 0)
- C (2, 0)
- D (4, 0)
- E (6, 0)
Intermediate Mathematical Challenge 2012, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C (2, 0)
After traversing the first semicircle, Peri will be at the point (8, 0); after the second semicircle Peri will be at (4, 0) and after the third semicircle, Peri will be at the point (2, 0).
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).