The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF.
Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ
Can you work out the area of the inner square and give an
explanation of how you did it?
LOGO Challenge - the Logic of LOGO
Age 11 to 16 Challenge Level:
We do not offer LOGO programs as solutions because there are so
many ways to tackle the challenges. You will know if you have the
correct solution because you will be able to create the pattern in
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.