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Triangle Center

See how to use the properties of a triangle center
(circumcenter/incenter/centroid/orthocenter).
5 examples and their solutions.

Circumcenter of a Triangle

Definition

The circumcenter of a triangle
is the center of the circle
that circumscribes the inner triangle.

Property

Three perpendicular bisectors of the sides
meet at the circumcenter.

Example

Point O is the circumcenter of △ABC.
BC = ?

Solution

Incenter of a Triangle

Definition

The incenter of a triangle
is the center of the circle
that inscribes the outer triangle.

Property

Three angle bisectors of the interior angles
meet at the incenter.

Example

Point O is the incenter of △ABC.
m∠OCB = ?

Solution

Centroid of a Triangle

Formula


M(x1 + x2 + x33, y1 + y2 + y33)
The coordinates of the centroid
is the mean of the vertices of a triangle.

Example

Solution

Property

Three medians of a triangle
meet at the centroid.
The centroid divides each median
in the ratio of 2 : 1.

Example

Point M is the centroid of △ABC.
x, y = ?

Solution

Orthocenter of a Triangle

Definition

Example

Orthocenter of △ABC?

Solution