HJB --- GMA --- UFF

(CEVAPOINT OF X(108) AND X(109))

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Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/(sin 2B - sin 2C) : 1/(sin 2C - sin 2A) : 1/(sin 2A - sin 2B)
                                    = f(a,b,c) : f(b,c,a) : f(c,a,b) , where f(a,b,c) = 1/[(b2 - c2)(b2 + c2 - a2)]

Barycentrics    a/(sin 2B - sin 2C) : b/(sin 2C - sin 2A) : c/(sin 2A - sin 2B)

X(162) lies on these lines:
4,270    6,1013    19,897    27,673    28,88    29,58    31,92    47,158    63,204    100,112    107,109    108,110    190,643    238,415    240,896    242,422    255,1099    412,580    799,811

X(162) = isogonal conjugate of X(656)
X(162) = X(250)-Ceva conjugate of X(270)
X(162) = cevapoint of X(I) and X(J) for this (I,J): (108,109)
X(162) = X(I)-cross conjugate of X(J) for these (I,J): (108,107), (109,110)
X(162) = crosssum of X(810) and X(822)
X(162) = X(I)-aleph conjugate of X(J) for these (I,J): (28,1052), (107,920), (162,1), (648,63)
X(162) = trilinear pole of line X(1)X(19)
X(162) = trilinear product of X(1113) and X(1114)

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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