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.
Argument | Reason | |
---|---|---|
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 |