TriangleCenter
TriangleCenter[tri,type]
gives the specified type of center for the triangle tri.
TriangleCenter[tri]
gives the centroid of the triangle.
Details
- TriangleCenter gives a list of coordinates.
- 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 GeometricScene, 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 form that specifies 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
open all close allBasic Examples (2)
Scope (12)
Calculate the endpoint of an angle bisector:
Calculate the centroid of a triangle:
Calculate the endpoint of a cevian passing through the orthocenter:
Calculate the endpoint of a cevian passing through a different vertex:
Calculate the endpoint of a cevian through an arbitrary center point:
Calculate the circumcenter of a triangle:
Calculate the excenter of a triangle at the specified vertex:
Calculate all of the excenters:
Calculate the foot of an altitude of a triangle at the specified vertex:
Calculate the incenter of a triangle:
Calculate the midpoint of a side of a triangle:
Calculate the nine-point center of a triangle:
Calculate the orthocenter of a triangle:
Properties & Relations (20)
Angle Bisector and Incenter (3)
An angle bisector endpoint is the intersection of an angle bisector and the opposite side:
The angle bisectors of a triangle intersect at the incenter:
TriangleConstruct[{a,b,c},"Incircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"Incenter"],TriangleMeasurement[{a,b,c},"Inradius"]]:
Median, Midpoint and Centroid (3)
A median intersects the opposite side at the midpoint:
The medians of a triangle intersect at the centroid:
TriangleCenter[{a,b,c}] is equivalent to RegionCentroid[Triangle[{a,b,c}]]:
Perpendicular Bisector, Midpoint and Circumcenter (3)
The perpendicular bisector of a side passes through the midpoint of that side:
The perpendicular bisectors of a triangle intersect at the circumcenter:
TriangleConstruct[{a,b,c},"Circumcircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"Circumcenter"],TriangleMeasurement[{a,b,c},"Circumradius"]]:
Altitude, Foot and Orthocenter (2)
Symmedian, Median and Angle Bisector (3)
Exterior Angle Bisector and Excenter (2)
The excenter opposite a vertex is the intersection of the exterior angle bisectors of the opposite angles:
TriangleConstruct[{a,b,c},"Excircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"Excenter"],TriangleMeasurement[{a,b,c},"Exradius"]]:
Nine-Point Circle, Foot, Midpoint, Orthocenter (2)
The nine-point circle of a triangle passes through the feet of the altitudes, the midpoints of the sides and the midpoints of the segments from the vertices to the orthocenter:
TriangleConstruct[{a,b,c},"NinePointCircle"] is equivalent to Circle[TriangleCenter[{a,b,c},"NinePointCenter"],TriangleMeasurement[{a,b,c},"NinePointRadius"]]:
Euler Line, Centroid, Circumcenter, Orthocenter and Nine-Point Center (1)
Midpoint (1)
TriangleCenter[{a,b,c},"Midpoint"] is equivalent to Midpoint[{a,c}]:
Text
Wolfram Research (2019), TriangleCenter, Wolfram Language function, https://reference.wolfram.com/language/ref/TriangleCenter.html.
CMS
Wolfram Language. 2019. "TriangleCenter." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TriangleCenter.html.
APA
Wolfram Language. (2019). TriangleCenter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TriangleCenter.html