Square Inscribed in a Circle

Circle, Square

Explore the geometric properties of a square inscribed in a circle.

Summarize the properties of squares, circles, diameters, chords,and how they would relate if the square is inscribed in a circle, before you start your actual construction.  Hint: If you are not familiar with the steps necessary for inscribing square in a circle construction, you might want to explore the applet below. Just use the buttons of the Navigation Bar in order to replay the construction steps.


Construct a square inscribed within a circle by following the construction steps provided below.

Construction Steps:

1.Toolbar ImageConstruct a circle with center A through B. (circle c) 6.Construct a circle with the center at point B and radius of f+.5. (circle e)
2.Toolbar ImageConstruct segment AB. (segment f) 7.Toolbar ImageConstruct the intersection points between circles d & e. (points D & E)
3.Toolbar ImageConstruct line AB. (line g) 8.Toolbar ImageConstruct line DE. (line h)
4.Toolbar ImageConstruct the intersection point between line g and circle c. (point C) 9. Toolbar ImageConstruct the intersection points between line h and circle c. (points G & F)
5.Construct a circle with the center at point C and radius of f+.5. (circle d) 10.Toolbar ImageDraw Quadrilateral BFCG. (poly1)