Library / UKMT Senior Kangaroo /63 of 139

UKMT Senior Kangaroo, 2020

Geometry Difficulty 2.0 Junior Prove it United Kingdom

A circle is drawn inside a regular hexagon so that it touches all six sides of the hexagon. The area of the circle is $\pi \times 64\sqrt{3}$ . What is the area of the hexagon?

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.