# Circumcenter Construction

- Author:
- Edward Knote

## Explore the construction of the circumcenter and its relationship with the triangle.

Summarize the properties and construction of the circumcenter of a triangle.

__Hint__: If you are not familiar with the construction steps necessary, 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 the circumcenter of triangle ABC by following the construction steps provided below the blank worksheet.

## 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) | | | |

## 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.)