Inscribed and circumscribed circles

Every triangle has a unique inscribed circle (incircle) and a unique circumscribed circle (circumcircle). The center of the incircle (incenter) is the point where the angle bisectors meet. The center of the circumcircle (circumcenter) is where the perpendicular bisectors of the sides meet.

Important properties

• The incenter is always inside the triangle.

• The circumcenter can be inside, on, or outside the triangle, depending on the triangle's type.

• The radius of the incircle is called the inradius; the radius of the circumcircle is called the circumradius.

• The incircle touches each side of the triangle exactly once.

• The circumcircle passes through all three vertices of the triangle.