Incenter | 合法醫療器材資訊網

由EWWeisstein著作·2003—TheincenterliesontheNagellineandSoddyline,andliesontheEulerlineonlyforanisoscelestriangle.TheincenteristhecenteroftheAdams'circle,Conway ...

The incenter is the center of the incircle[1] for a polygon or insphere[2] for a polyhedron (when they exist). The corresponding radius of the incircle[3] or insphere[4] is known as the inradius[5].

The incenter can be constructed as the intersection of angle bisectors[6]. It is also the interior point for which distances to the sides of the triangle are equal. It has trilinear coordinates[7] 1:1:1, i.e., triangle center function[8]

(1)

and homogeneous barycentric coordinates[9] . It is Kimberling center[10] .

For a triangle[11] with Cartesian vertices , , , the Cartesian coordinates[12] of the incenter are given by

(2)

The distance between the incenter and circumcenter[13] is , where is the circumradius[14] and is the inradius[15], a result known as the Euler triangle formula[16].

The incenter lies on the Nagel line[17] and Soddy line[18], and lies on the Euler line[19] only for an isosceles triangl...