CEMC Cayley, 2002

Geometry Difficulty 2.0 Junior Find the answer Canada

In the diagram, the circle has centre $O$ . The shaded sector $AOB$ has sector angle $90^\circ$ , and $AB$ has arc length $2\pi$ units. The area of sector $AOB$ is

(A) $4\pi$ (B) $16\pi$ (C) $6\pi$ (D) $24\pi$ (E) $8\pi$

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.