You may also like

Mean Geometrically

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

Logosquares

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

Cut Cube

Age 16 to 18
Challenge Level

Points P, Q and R are drawn on a cube, one third of the way along the edges AB, GH and ED respectively, as shown in the diagram. The cube is then cut along the plane PQR. Which slice, if any, has the greater volume? Describe the shape and symmetries of the pieces obtained.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
Copyright © 1997 - 2023. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.