# Points of Concurrency

- Author:
- Matthew Desjardins, powere

Find the perpendicular bisector between the two Lowe's locations.

This third red dot represents a different chain. Recall that the perpendicular bisector helps find equidistance between points, in this case the Lowe's stores. Your perpendicular bisector should nearly pass through this store. What store do you think this is? Why would they put it here?

## Perpendicular Bisectors, Circumcenter, and Circumcircle

Construct the 3 Perpendicular Bisectors of each triangle
Construct the point of concurrency (circumcenter which is the intersection of the three lines) for each triangle.
Construct the Circumcircle (center at the circumcenter and passing through the vertices).

The Circumcenter (point of intersection of the 3 perpendicular bisectors) is located __________________.

## Angle Bisectors, Incenter, and Incircle

Construct the 3 Angle Bisectors of each triangle
Construct the point of concurrency (incenter which is the intersection of the three lines) for each triangle.
Construct the perpendicular line from the incenter to one of the sides. Mark the intersection at the right angle where the two lines meet.
Construct the Incircle (center at the incenter and the point identified on the last step).

The Incenter (point of intersection of the 3 angle bisectors) is located __________________.

## Medians and centriods

Construct the 3 Medians of each triangle (find the midpoint of each side and connect to the opposite vertex.
For Triangle ABC, mark the centroid (point of concurrency) as point X and the intersection on SegmentBC as point Y.
Measure AX
Measure XY.
Calculate 2*XY. What do you notice?
For Triangle DEF, mark the Centroid

The Centriod (point of intersection of the 3 medians) is located __________________.

## Altitudes and Orthocenters

Construct the 3 Altitudes of each triangle (Perpendicular from a vertex to the opposite side)
Construct the point of concurrency (orthocenter: which is the intersection of the three lines) for each triangle.

The Orthocenter (point of intersection of the 3 Altitudes) is located __________________.