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Fitting In

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

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Look Before You Leap

Can you spot a cunning way to work out the missing length?

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Triangle Midpoints

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:

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 picture:
anamorphic picture