Form inward semicircles (orange) and outward semicircles (purple) on two opposite sides of a quadrilateral. Connect the midpoints of the orange arcs, intersecting with the purple arcs. Show that you obtain two corners of an enclosing square.

As pointed out by Lewis Corner, the construction produces a square but it does not necessarily contain the quadrilateral inside its boundaries. However each vertex of the quadrilateral will be on one of the lines extending one of the squareâ€™s sides.

## One reply on “Squaring the quad”

As pointed out by Lewis Corner, the construction produces a square but it does not necessarily contain the quadrilateral inside its boundaries. However each vertex of the quadrilateral will be on one of the lines extending one of the squareâ€™s sides.