You may also like

problem icon

Doodles

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

problem icon

Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

problem icon

Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Long Short

Age 14 to 16 Challenge Level:
Quadrilateral in a circle
Draw a circle with radius $1$ unit. Choose any four points on the circumference and join them together to form a quadrilateral.

Label the sides: $a$ is the shortest, $b$ is the next shortest, then $c$, and finally $d$ is the longest side (it is possible to have two sides of equal length).

What is the maximum length that the shortest side $a$ could be?

Side $b$ must be less than a certain value - what value?

What is the maximum length that the longest side $d$ could be? Is it possible for $c$ and $d$ both to be this maximum length?