Special Centers in a Triangle

Centroid

Centroid is the point of intersection of all the medians of a triangle. It is the geometric of a plane figure.

Incenter

Incenter is the point of intersection of all angle bisectors in a triangle. It is also the center of the inscribed circle (incircle) in a triangle.

where A = area of the triangle and s = ½ (a + b + c).

• See the derivation of formula for radius of incircle.

Circumcenter

Circumcenter is the point of intersection of all perpendicular bisectors of a triangle. It is also the center of the circumscribed circle (circumcircle).

where R = radius of Circumscribed Circle and a, b and c are the sides.

Orthocenter

Orthocenter is the point of intersection of all the altitudes of a triangle. Like circumcenter, it can be inside or outside the triangle.

Excenter

Excenter is the center of the escribed circle.

TRIVIA

A line that passes through the incenter and orthocenter of a triangle is called Euler's line.

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