Library / UKMT Intermediate Mathematical Challenge /201 of 267

UKMT Intermediate Mathematical Challenge, 2017

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows an arc $PQ$ of a circle with centre $O$ and radius $8$ . Angle $QOP$ is a right angle, the point $M$ is the midpoint of $OP$ and $N$ lies on the arc $PQ$ so that $MN$ is perpendicular to $OP$ . Which of the following is closest to the length of the perimeter of triangle $PNM$ ?

(A) $17$ (B) $18$ (C) $19$ (D) $20$ (E) $21$

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.