Library / UKMT Senior Mathematical Challenge /44 of 212

UKMT Senior Mathematical Challenge, 2021

Geometry Difficulty 1.0 Junior Find the answer United Kingdom

Three points, $P$ , $Q$ and $R$ are placed on the circumference of a circle with centre $O$ . The arc lengths $PQ$ , $QR$ and $RP$ are in the ratio $1 : 2 : 3$ . In what ratio are the areas of the sectors $POQ$ , $QOR$ and $ROP$ ?

(A) $1 : 1 : 1$ (B) $1 : 2 : 3$ (C) $1 : \pi : \pi^2$ (D) $1 : 4 : 9$ (E) $1 : 8 : 27$

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.