incenter's Usage Examples:

In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement.

The center of the incircle is a triangle center called the triangle's incenter.

incircle of the quadrilateral or its inscribed circle, its center is the incenter and its radius is called the inradius.

where I is the incenter.

The incenter lies on the median.

and center of these circles are called inradius and circumradius, and incenter and circumcenter respectively.

For example the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained.

conjugate of the incenter of a triangle ABC is the incenter itself.

So the antiorthic axis, which is the central line associated with the incenter, is the axis.

The Nagel point, the centroid, and the incenter are collinear on a line called the Nagel line.

The incenter is the Nagel point of the medial triangle;.

identified by an index number of the form X(n)—for example, X(1) is the incenter.

AB, respectively The Neuberg cubic passes through the following points: incenter, circumcenter, orthocenter, both Fermat points, both isodynamic points.

point on which the triangle would balance if it had uniform density; the incenter, the center of the circle that is internally tangent to all three sides.

Its center, the Spieker center, in addition to being the incenter of the medial triangle, is the center of mass of the uniform-density boundary.

Guinand showed in 1984 that the triangle's incenter must lie in the interior of the orthocentroidal circle, but not coinciding.

discovered only in 1986, unlike the classical triangle centers like centroid, incenter, and Steiner point.

The incenter of this common orthic triangle must be one of the original four orthocentric.

They all meet at the incenter.

The Nagel point of the medial triangle is the incenter of its reference triangle.

bases are collinear with the incenter.

In a tangential trapezoid, the midpoints of the legs are collinear with the incenter.

Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by d 2 = R ( R − 2 r ) {\displaystyle d^{2}=R(R-2r)}.

circle that cannot be the incenter is the nine-point center, and every other interior point of the circle is the incenter of a unique triangle.