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
The diagonals of a square meet at O. The bisector of angle OAB meets BO and BC at N and P respectively. The length of NO is 24. How long is PC?
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?
Using a ruler and compass only it is possible to
fit a square into any triangle so that one side of the square rests
on one side of the triangle and the other two vertices of the
square touch the other two sides of the triangle:
How is this possible?
Prove why this works.
It is easy to draw a square ABCD with BC on the
base PR of the triangle and the vertex D on the side PQ
What happens to the point A as you enlarge the
square? The interactivity may help.