Square Inscribed in a Circle
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) | 10. |  | Draw Quadrilateral BFCG. (poly1) |