CEMC Fermat, 2009

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, the circle and the square have the same centre $O$ and equal areas. The circle has radius 1 and intersects one side of the square at $P$ and $Q$ . What is the length of $PQ$ ?

(A) $\sqrt{4-\pi}$ (B) $1$ (C) $\sqrt{2}$ (D) $2-\sqrt{\pi}$ (E) $4-\sqrt{\pi}$

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: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.