# Circumcircle of a Triangle Construction

## Explore the construction of the circumcircle of a triangle

If you are not familiar with the construction steps necessary for the construction of the circumcircle of a triangle, 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 circumcircle of a triangle that passes the

*Drag Test*by following the construction steps provided below.## Try it yourself...

## Construction steps

1. | Create an arbitrary triangle ABC. | |

2. | Construct the Perpendicular Bisector for each side of the triangle.
Hint: The tool Perpendicular Bisector can be applied to an existing segment. | |

3. | Create intersection point D of two of the line bisectors.
Hint: The tool Intersect can be applied to the intersection of three lines or by successively selecting two of the three line bisectors. | |

4. | Construct a circle with center D through one of the vertices of triangle ABC. | |

5. | Perform the Drag Test to check if your construction is correct. |

6. | Activate the Move tool and select point D. | |

7. | Start typing the new name on the keyboard in order to open the `Circumcenter` Rename dialog.
| |

8. | Select OK to apply your changes and rename the point. |

## Use your construction to answer the following questions

Can the circumcenter of a triangle lie outside the triangle? If yes, for which types of triangles is this true?

Try to think of a real world application in which finding the circumcenter of a triangle would be useful.