TOPICS
Search

Major Triangle Center


A triangle center alpha:beta:gamma is called a major triangle center if the triangle center function alpha=f(a,b,c,A,B,C) is a function of angle A alone, and therefore beta and gamma of B and C alone, respectively. The following table summarizes a number of major triangle centers.

Kimberling centertriangle centertriangle center function
X_1incenter1
X_3circumcentercosA
X_4orthocentersecA
X_(13)Fermat pointcsc(A+pi/3)
X_(14)2nd isogonic centercsc(A-pi/3)
X_(15)1st isodynamic pointsin(A+pi/3)
X_(16)2nd isodynamic pointsin(A-pi/3)
X_(17)1st Napoleon pointcsc(A+pi/6)
X_(18)2nd Napoleon pointcsc(A-pi/6)
X_(19)Clawson pointtanA
X_(24)perspector of abc and orthic-of-orthic trianglecos(2A)secA
X_(25)homothetic center of orthic and tangential trianglessinAtanA
X_(33)perspector of the orthic and intangents triangles1+secA
X_(34)1-secA
X_(35)1+2cosA
X_(36)inverse of the incenter in the circumcircle1-2cosA
X_(47)cos(2A)
X_(48)sin(2A)
X_(49)center of sine-triple-angle circlecos(3A)
X_(50)sin(3A)
X_(61)sin(A+pi/6)
X_(62)sin(A-pi/6)
X_(63)cotA
X_(68)cosAsec(2A)
X_(77)1/(1+secA)
X_(78)1/(1-secA)
X_(79)1/(1+2cosA)
X_(80)reflection of incenter about Feuerbach point1/(1-2cosA)
X_(91)sec(2A)
X_(92)Ceva point of incenter and Clawson pointcsc(2A)
X_(93)sec(3A)
X_(94)csc(3A)

See also

Kimberling Center, Regular Triangle Center, Triangle Center

Explore with Wolfram|Alpha

References

Kimberling, C. "Major Centers of Triangles." Amer. Math. Monthly 104, 431-438, 1997.

Referenced on Wolfram|Alpha

Major Triangle Center

Cite this as:

Weisstein, Eric W. "Major Triangle Center." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MajorTriangleCenter.html

Subject classifications