How to construct a square inscribed in a given circle. The construction proceeds as follows:
If the circle's center point is not given, it can be constructed using the method in Constructing the center of a circle.
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
|1||AC is a diameter of the circle O||A diameter is a line through the circle center. See Diameter definition.|
|2||BD is a diameter of the circle O||It was drawn using the method in Perpendicular bisector of a line. See that page for proof. The center of a circle bisects the diameter, so BD passes through the center.|
|3||AC, BD are perpendicular||BD was drawn using the method in Perpendicular bisector of a line. See that page for proof.|
|4||AC, BD bisect each other||Both are diameters of the circle O. (1), (2) and the center of a circle bisects its diameter. See Diameter definition|
|5||ABCD is a square||Diagonals of a square bisect each other at 90°. (3), (4)|
|6||ABCD is an inscribed square||All vertices lie on the given circle O|