HJB --- GMA --- UFF


Click here to access the list of all triangle centers.

Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon Run Macro Tool, select the center name from the list and, then, click on the vertices A, B and C successively.

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Download all construction files and macros: (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..

Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - 2a)/ (b + c - a)
                                    = g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 2 - 2 cos A - cos B - cos C (Peter J. C. Moses)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Let X'Y'Z' be the pedal triangle of the Bevan point, W = X(40); then X(1319) is the point, other than W, in which the circles AWX', BWY', CWZ' concur. (Floor van Lamoen, Hyacinthos #6321, 6352).

X(1319) lies on these lines:
1,3    11,515    12,1125    37,604    44,1317    48,1108    59,518    73,1104    77,1122    106,1168    108,953    210,956    214,519    226,535    355,499    392,993    513,663    529,908    840,934    910,1055    961,1255

X(1319) is the {X(1),X(56)}-harmonic conjugate of X(65).

X(1319) = midpoint of X(1) and X(36)
X(1319) = reflection of X(1155) in X(36)
X(1319) = isogonal conjugate of X(1320)
X(1319) = inverse-in-circumcircle of X(56)
X(1319) = inverse-in-incircle of X(65)
X(1319) = cevapoint of X(902) and X(1404)
X(1319) = crosspoint of X(1) and X(104)
X(1319) = crosssum of X(1) and X(517)
X(1319) = crossdifference of any two points on line X(9)X(650)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense

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