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            bc/(b + c - 2a) : ca/(c + a - 2b) : ab/(a + b - 2c)
Barycentrics    1/(b + c - 2a) : 1/(c + a - 2b) : 1/(a + b - 2c) (Darij Grinberg, 12/28/02)

James Blaikie (1847-1929) proposed the following problem. Let O be any point in the plane of triangle ABC, and let any straight line g through O meet BC in P, CA in Q, AB in R; then, if points P', Q', R' be taken on the line so that

                     PO = OP',       QO = OQ',       RO = OR',

prove that AP', BQ', CR' are concurrent.

Darij Grinberg introduces the term Blaikie point of O and g for the point Z of concurrence. If

                     O = x : y : z and g = [k : l : m] (barycentric coordinates),

then Z has first barycentric 1/[k(y-z) - (ly-mz)]. Given a point S = u : v : w, Grinberg then defines the S-Blaikie transform of O as the Blaikie point of O and OS. The first barycentric of Z can be written as

                     1/[yw(y+x) + zv(z+x) - yz(2u+v+w)].

Visit Blaikie theorem in barycentrics. (Darij Grinberg, 12/28/02)

X(903) lies on these lines:
2,45    7,528    27,648    75,537    86,99    310,670    320,519    335,536    350,889    527,666    675,901    812,1022

X(903) = reflection of X(I) in X(J) for these (I,J): (2,1086), (3,190)
X(903) = isogonal conjugate of X(902)
X(903) = isotomic conjugate of X(519)
X(903) = X(I)-cross conjugate of X(J) for these (I,J): (320,86), (519,2)

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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