INSTITUTO DE MATEMÁTICA
HJB --- GMA --- UFF

X(372)
({X(3),X(6)}-HARMONIC CONJUGATE OF X(371))


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: tc.zip (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           cos(A + π/4) : cos(B + π/4) : cos(C + π/4)
                                    = cos A - sin A : cos B - sin B : cos C - sin C

Barycentrics    sin A cos(A + π/4) : sin B cos(B + π/4) : sin C cos(C + π/4)

X(372) is the external center of similitude of the circumcircle and the 2nd Lemoine circle (cosine circle) (Peter J. C. Moses, 5/9/03). Also, X(372) is the external center of similitude of the Gallatly circle (defined just before X(2007)) and the 1st Lemoine circle (Peter J. C. Moses, 9/10/03).

For details and references, see X(371).

X(372) lies on these lines:
2,485    3,6    4,486    25,494    193,487    315,492    601,605    602,606

X(372) = reflection of X(I) in X(J) for these (I,J): (315,639), (371,32), (638,640)
X(372) = isogonal conjugate of X(486)
X(372) = inverse-in-Brocard-circle of X(371)
X(372) = inverse-in-1st-Lemoine-circle of X(2462)
X(372) = complement of X(638)
X(372) = anticomplement of X(640)
X(372) = X(4)-Ceva conjugate of X(371)

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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