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
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
It Depends on Your Point of View!
Age 14 to 16 Challenge Level:
Preveina explained how she drew an image on a $4
\times 4$ square grid and then distorted the grid to distort her
image. Here is her distorted grid:
Preveina noted that the process of creating a
grid for a piece of anamorphic art uses similar mathematical skills
to the process of enlarging a shape.
Timothy sent us a picture he created using the
techniques of anamorphosis, although he did not send us an
explanation of how he created his image, or which position it
should be viewed from in order to see it correctly. Here is his
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.