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
Which has the greatest area, a circle or a square inscribed in an
isosceles, right angle triangle?
Four identical right angled triangles are drawn on the sides of a
square. Two face out, two face in. Why do the four vertices marked
with dots lie on one line?
Just using coordinates and the clue in the
original diagram there is a short and sweet solution sent in by Jo
By concentrating on the geometry, she made the
algebra very simple. With the clue that $p-q = a-c$ and $p+q=b-d$
she was able to find the area of the square $ABCD$: