Square with a Compass

1. Construct a square with only a compass and a straightedge.
2. Construct a 2 inch square with only a compass and a straightedge, with the compass stuck at a distance of 2 inches.
3. Mark the four corners of a square using only a compass.

Source: rec.puzzles, Original, Henry Ernest Dudeny.

1. Draw a circle (c) with center O.
   A diameter through O cuts (c) at the points A and B.
   Draw the perpendicular bisector of AB which cuts (c) at the points C and D.
   ABCD is a square.

2. Here is a solution giving a square of side 2 and a square of area 2.
   Draw a circle (c) of center O and radius 2.
   Draw a point Q on (c).
   Determine on (c) the points J and K such as QJ = QK = 2.
   Determine on (c) the point L such that JL=2.
   The circles of centers J and L meet at O and O'.
   OO' which is the perpendicular bisector of JL, cuts (c) at the point S.
   Square of side 2:
   Draw the circles of centers Q and S with radius 2.
   They meet at a point T symmetrical of O about QS. OSTQ is a square of side 2.

   Square of area 2:
   JK and QS meet at P.
   Determine the point R on JK such as PR = 2.
   OPQR is a square whose the diagonals are perpendicular and equal to 2. The area of this square is equal to 2.

3. Draw a circle (c) with center A and radius 1.
   Draw B on (c).
   The circle of center B and radius 1, cuts (c) at C and D.
   The circle of center C and radius 1, cuts (c) at B and E.
   The circles of centers D and E with radius equal to DC = EB = sqrt(3) meet themselves at F.
   The circle of center D and radius AF = sqrt(2) cuts (c) at G on the middle of the arch CB.
   The circles of centers D and G and radius 1 cut at H.
   ADHG is a square of side 1.