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Square inscribed in a circle

Definition: A square where all four vertices lie on a common circle.
Try this Drag the orange dot A. Note how the four vertices of the square always lie on the circle.

A square inscribed in a circle is one where all the four vertices lie on a common circle. Another way to say it is that the square is 'inscribed' in the circle. Here, inscribed means to 'draw inside'.

Diagonals

The diagonals of a square inscribed in a circle intersect at the center of the circle. To see this check the 'diagonals' box in the applet above. As with all squares, the diagonals bisect each other at right angles.

Circumcircle

Another way to think of this is that every square has a circumcircle - a circle that passes through every vertex. In fact every regular polygon has a circumcircle, and so can be inscribed in that circle.

Construction

You can construct a square inscribed in a circle using compasses and a straightedge. For more see Constructing an inscribed square.

Other polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons