# Points of Concurrency

- Author:
- Stephen Greene

## On this page you will explore different points of concurrency.

A

**point of concurrency**is a point where three or more lines intersect. A**circumcenter**is made by constructing all the**perpendicular bisectors**of a triangle. A very useful characteristic of a circumcenter is that it is**equidistant to the verticies**of a triangle. This is shown by making a circle that goes all the way around it and through all of the verticies.## Construct your own circumcenter

1. | Select tool Polygon. Create an arbitrary triangle ABC by clicking three times in the Graphics View. Close the triangle by selecting the first point A again. | |

2. | Activate tool Perpendicular Bisector. Construct the Perpendicular Bisector for two of the edges of the triangle by successively selecting the segments.
Hint: You can find this tool in the Special Lines Toolbox (fourth Toolbox from the left). | |

3. | Create intersection point D of the two the line bisectors.
Hint: Successively select the two line bisectors, or click directly on the intersection point. | |

4. | Construct a circle with center D through one of the vertices of triangle ABC.
Hint: First, select point D, then, for example, point A. | |

5. | Select the Move tool and drag the vertices of the triangle in order to check if your construction is correct. |

A reminder, a

**point of concurrency**is a point where three or more lines intersect. An**incenter**is made by constructing all the**anglel bisectors**of a triangle. A very useful characteristic of a circumcenter is that it is**equidistant to the sides**of a triangle. This is shown by making a circle that goes stays inside the triangle and intersects all three in just one point each.## Incenter Use the arrows in the bottom right to go through step by step.

## Construct your own incenter

1. | Select tool Polygon. Create an arbitrary triangle ABC by clicking three times in the Graphics View. Close the triangle by selecting the first point A again. | |

2. | Activate tool Angle Bisector. Construct the Angle Bisector for each angle of the triangle.
Hint: You can find this tool in the Special Lines Toolbox (fourth Toolbox from the left). | |

3. | Create intersection point D of the line bisectors.
Hint: Successively select the line bisectors, or click directly on the intersection point.
| |

4. 5. 6. |
Activate tool Perpendicular Line. Construct a Perpendicular Line by selecting the Incenter made in step 3 and then a side of the triangle. Repeat this for each side of the triangle.
Create the intersection of the Perpendicular Lines made in step 4 and the sides of the triangle.
Construct a circle with center D through one of the intersection points made in step 5.
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7. | Select the Move tool and drag the vertices of the triangle in order to check if your construction is correct. |