Library / UKMT Senior Mathematical Challenge /123 of 212

UKMT Senior Mathematical Challenge, 2016

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The circumference of a circle with radius 1 is divided into four equal arcs. Two of the arcs are 'turned over' as shown. What is the area of the shaded region?

(A) $1$ (B) $\sqrt{2}$ (C) $\frac{1}{2}\pi$ (D) $\sqrt{3}$ (E) $2$

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.