# 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:

 In:= Out= In:= Out= Calculate the excenter of a triangle at the specified vertex:

 In:= Out= In:= Out= ## Properties & Relations(28)

Introduced in 2019
(12.0)