Library / UKMT Senior Mathematical Challenge /140 of 212

UKMT Senior Mathematical Challenge, 2022

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A square is inscribed inside a quadrant of a circle. The circle has radius $10$ . What is the area of the square?

(A) $25\sqrt{2}$ (B) $36$ (C) $12\pi$ (D) $40$ (E) $30\sqrt{2}$

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.