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.

Task

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

Construction Steps:

1.

Construct 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.

Construct segment AB. (segment f)

7.

Construct the intersection points between circles d & e.
(points D & E)

3.

Construct line AB. (line g)

8.

Construct line DE. (line h)

4.

Construct the intersection point between line g and circle c. (point C)

9.

Construct 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)