TriangleCenter

TriangleCenter[tri,type]

gives the specified type of center for the triangle tri.

Details

  • The triangle tri can be given as {p1,p2,p3}, Triangle[{p1,p2,p3}] or Polygon[{p1,p2,p3}].
  • The following center types can be given:
  • {"AngleBisectingCevianEndpoint",p}endpoint of the cevian bisecting the angle at the vertex p
    "Centroid"centroid
    {"CevianEndpoint",center,p}endpoint of the cevian passing through the vertex p and the specified center
    "Circumcenter"center of the circumcircle
    {"Excenter",p}center of the excircle opposite from the vertex p
    {"Foot",p}foot of the altitude passing through the vertex p
    "Incenter"center of the incircle
    {"Midpoint",p}midpoint of the side opposite from the vertex p
    "NinePointCenter"center of nine-point circle
    "Orthocenter"orthocenter
    {"SymmedianEndpoint",p}endpoint of the symmedian passing through the vertex p
    "SymmedianPoint"symmedian point
  • In the form {"type",p}, p can be a symbolic point specification in a geometric scene, or it can be an explicit vertex of the form {x,y}, Point[{x,y}] or the index i of the vertex. When given in the short form "type", the vertex p2 is used.
  • In the form {"CevianEndpoint",center,p}, the center can be given as a center type such as "Centroid" or as a point specification. When given in the short form {"CevianEndpoint",center}, the vertex p2 is used.
  • In any type that takes a vertex p, a value of All will return a list of three values corresponding to the vertices.
  • TriangleCenter can be used with symbolic points in GeometricScene.

Examples

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Basic Examples  (2)

Find the incenter of a triangle:

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Calculate the incenter of a triangle:

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Calculate the excenter of a triangle at the specified vertex:

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Specify a different vertex:

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Calculate all of the excenters:

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Scope  (12)

Properties & Relations  (20)

Introduced in 2019
(12.0)