### 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

### Look Before You Leap

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

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second wall. At what height do the ladders cross?

# Squirty

##### Stage: 4 Challenge Level:

Can you draw a square  ABCD with BC on the base PR of the triangle and the vertex D on the side PQ using ruler and compasses?

What happens to the point A as you enlarge the square? The interactivity may help.

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How can you use this to help you draw the square you require?