#### Transcript of Points of Concurrency in a Triangle

INCENTER

CENTROID

Circumcenter

**Points of Concurrency in a Triangle**

ORTHOCENTER

How do you find it?

Construct the angle bisectors.

angle bisector divides an angle in two equal parts

Special properties:

1. Equidistant from the sides of the triangle.

2. Center of an inscribed circle (measure the perpendicular distance from the incenter to the side)

Location: Always inside the triangle.

How do you find it?

Construct the perpendicular bisectors.

Perpendicular bisector: a line perpendicular to a line segment that passes through the midpoint.

Special Properties:

1. Equidistant from the vertices

2. Center of a circle circumscribed about the triangle.

Location:

Depends..,

Acute - inside

Obtuse - outside

Right - at the midpoint of the hypotenuse

How do you find it?

Point of concurrency of the three medians

Median: a segment connecting the midpoint of one side to the opposite vertex.

Special Properties:

1. Center of gravity for the triangular region

2. The dist. from vertex to centroid is twice the dist. from the centroid to the midpoint of the opposite side

Location:

Always inside the triangle

**How do you find it?**

Construct the altitudes.

Altitude:

A segment from the vertex perpendicular to the opposite side.

Special Properties:

None

Location:

Depends...

Acute - inside

Obtuse - outside

Right - on the vertex of the right angle.

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