Circumcenter Construction
Review of constructing a Perpendicular Bisector
Construction Steps:
| 1. |  | Construct a circle centered at point A and through point B. (circle d) | 8. |  | Construct line GF. (line i) | |
| 2. |
| Construct a circle centered at point B and through point A. (circle e) | 9. | | Construct a circle centered at point B and through point C. (circle k) | |
| 3. |  | Construct the intersection points between circle d and circle e. (point D & point E) | 10. | | Construct a circle centered at point C and through point B. (circle p) | |
| 4. | | Construct line DE. (line f) | 11. | | Construct the intersection points between circle k and circle p. (point I & point H) | |
| 5. | | Construct a circle centered at point A and through point C. (circle g) | 12 | | Construct line IH. (line J) |
| 6. | | Construct a circle centered at point C and through point A. (circle h) | 13. | | Construct the intersection of line f and line i. (point J) | |
| 7. | | Construct the intersection points between circle g and circle h. (point G & point F) | | | |
Task:
Construct the circumcenter of triangle ABC by following the construction steps provided above the blank worksheet.
Question:
Are line DE, line GF, and line IH always concurrent? (Move points A, B, and C to change the triangle and check your answer.)
Explore the construction of the circumcenter and its relationship with the triangle.
Here is the finished construction