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$A$ and $C$ are the opposite vertices of a square $ABCD$, and
have coordinates $(a,b)$ and $(c,d)$, respectively.
What are the coordinates of the other two vertices?
What is the area of the square?
How generalisable are these results?
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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
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?