It is really easy and fast to draw a square inscribed in a circle using a straightedge and compass. You would only need to draw a line which would be the diameter of the circle and then draw a perpendicular to that line using the method of the compass and straightedge (putting one side of the compass in one extreme of the diameter, then opening up the compass to a point O farther that the center of the diameter and draw the line, then do the same from the other side of the diameter (without changing the width of the compass), the lines will bisect and these two points along with the extremes of the diameter will become the vertices of the inscribed square.
This method should take less than a minute to complete.
