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           sec(A + ω) : sec(B + ω) : sec(C + ω)
                                    = f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/(b4 + c4 - a2b2 - a2c2)

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = 1/(b4 + c4 - a2b2 - a2c2)

X(98) = circumcircle-antipode of X(99)
X(98) = the point of intersection, other than A, B, and C, of the circumcircle and Kiepert hyperbola.
X(98) = Ψ(X(101), X(100)

J. W. Clawson, "Points on the circumcircle," American Mathematical Monthly 32 (1925) 169-174.

X(98) lies on these lines:
2,110    3,76    4,32    5,83    6,262    10,101    13,1080    14,383    20,148    22,925    23,94    25,107    30,671    100,228    109,171    186,935    275,427    376,543    381,598    385,511    468,685    523,842    620,631    804,878

X(98) is the {X(2),X(147)}-harmonic conjugate of X(114). For a list of harmonic conjugates, click More at the top of this page.

X(98) = midpoint between X(20) and X(148)
X(98) = reflection of X(I) in X(J) for these (I,J): (4,115), (99,3), (147,114), (1513,230)
X(98) = isogonal conjugate of X(511)
X(98) = isotomic conjugate of X(325)
X(98) = complement of X(147)
X(98) = anticomplement of X(114)
X(98) = X(290)-Ceva conjugate of X(287)
X(98) = cevapoint of X(I) and X(J) for these (I,J): (2,385), (6,237)
X(98) = X(I)-cross conjugate of X(J) for these (I,J): (230,2), (237,6), (248,287), (446,511)
X(98) = crosssum of X(385) and X(401)
X(98) = X(2)-Hirst inverse of X(287)

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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