Library / UKMT Senior Kangaroo /92 of 139

UKMT Senior Kangaroo, 2021

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In the figure shown there are three concentric circles and two perpendicular diameters. The three shaded regions have equal area. The radius of the small circle is $2$ . The product of the three radii is $Y$ . What is the value of $Y^2$ ?

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.