You may also like
Some(?) of the Parts
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Ladder and Cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
Bendy Quad
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Age 14 to 16 Short
Challenge Level
The diagram shows a rectangle and two semicircles.
The height of the rectangle 10 cm, and the area of the shaded region is 125 cm$^2$.
What is the shortest distance between the two semicircles?
Give your answer in terms of $\pi$.
This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
Copyright © 1997 - 2023. University of Cambridge.
All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.