Copyright © University of Cambridge. All rights reserved.

## 'Long Short' printed from http://nrich.maths.org/

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?