UKMT Cayley Olympiad, 2022

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The regular octagon $ABCDEFGH$ is inscribed in a circle. Points $P$ and $Q$ are on the circle, with $P$ between $C$ and $D$ , such that $APQ$ is an equilateral triangle. It is possible to inscribe a regular $n$ -sided polygon, one of whose sides is $PD$ , in the circle. What is the value of $n$ ?

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.