**Incenter**

**Centroid**

**Circumcenter**

Points of Concurrency in a Triangle

How do you find it? Find the point of concurrency of the medians.

Special Properties:

1. The center of gravity for the triangular region.

2. The distance from the vertex to the centroid is twice the distance from the centroid to the side.

Location: Always inside the triangle.

Location:

Depends...

Obtuse - outside

Right - midpoint of the hypotenuse

Acute - inside

**How do you find it?point of concurrency**

of the perpendicular bisectors

of the perpendicular bisectors

Perpendicular bisector - perpendicular to a side and passing through the midpoint

Special Properties:

1. Equidistant to each vertex

2. You can make a circumscribe circle about the triangle or you can inscribe a triangle inside the circle.

How do you find it?

Point of concurrency of the angle bisectors

How do you find it?

Point of concurrency of the altitudes

Location:

Depends...

Acute - inside

Obtuse - outside

Right - on the right angle

Special

Properties:

None

**Orthocenter**

Altitude - perpendicular to a side and passing through the opposite vertex

Median: a line from the vertex to midpoint of opposite side

2. Center of the circle inscribed within the triangle (must construct the perpendicular segments to the sides to draw the circle)

Special Properties:

1. Equidistant from the vertices

Location:

Always inside the triangle.