Library / UKMT Intermediate Mathematical Challenge /236 of 267

UKMT Intermediate Mathematical Challenge, 2012

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

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) $(6,0)$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.