TriangleConstruct

TriangleConstruct[tri,type]

gives the specified type of construct 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 point 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
  • The following line types can be given:
  • {"Altitude",p}altitude passing through the vertex p
    {"AngleBisectingCevian",p}cevian bisecting the interior angle at the vertex p
    {"AngleBisector",p}bisector of the interior angle at the vertex p
    "Boundary"boundary
    {"Cevian",center,p}cevian passing through the vertex p and the specified center
    "EulerLine"Euler line
    {"ExteriorAngleBisector",p}bisector of the exterior angle at the vertex p
    {"Median",p}median passing through the vertex p
    {"OppositeSide",p}side opposite from the vertex p
    {"PerpendicularBisector",p}perpendicular bisector of the side opposite from p
    {"Symmedian",p}symmedian passing through the vertex p
  • The following circle types can be given:
  • "Circumcircle"circumscribed circle
    {"Excircle",p}excircle opposite from the vertex p
    "Incircle"inscribed circle
    "NinePointCircle"nine-point circle
  • The following triangle types can be given:
  • "AntimedialTriangle"antimedial triangle
    "MedialTriangle"medial triangle
    "Triangle"original triangle
  • 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 forms {"CevianEndpoint",center,p} and {"Cevian",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.
  • TriangleConstruct can be used with symbolic points in GeometricScene.

Examples

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Basic Examples  (2)

Calculate the altitude of a triangle:

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Calculate the excenter of a triangle at the specified vertex:

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Scope  (29)

Properties & Relations  (28)

Introduced in 2019
(12.0)