Suppose you are given a piece of tracing paper with a circle on it and you do not have a compass. How can you use paper folding to inscribe a square in the circle?
Fold the circle so that one half coincides with the other. The crease is a radius of the circle. Then
fold this crease onto itself to make a second crease that is the perpendicular trisector of the first.
These two creases intersect the circle at the vertices
of an inscribed square.