Library / UKMT Senior Mathematical Challenge /185 of 212

UKMT Senior Mathematical Challenge, 2025

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

The diagram shows three arcs of circles of radius 1. $P$ is the centre of the circle of which $RQ$ is an arc and $Q$ is the centre of the circle of which $PR$ is an arc. What is the area of this shape?

(A) $\frac{\sqrt{3}\pi}{10}$ (B) $\frac{\pi}{6}$ (C) $\frac{\pi}{8}$ (D) $\frac{\sqrt{3}}{4}$ (E) $\frac{\sqrt{2}\pi}{9}$

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.