Library / UKMT Junior Mathematical Olympiad /54 of 98

UKMT Junior Mathematical Olympiad, 2015

Geometry Difficulty 2.0 Junior Prove it United Kingdom

Two circles of radius $1$ cm fit exactly between two parallel lines, as shown in the diagram. The centres of the circles are $3$ cm apart. What is the area of the shaded region bounded by the circles and the lines?

Figure for this problem

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.