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

X(546)
(MIDPOINT OF X(4) AND X(5))


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           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 3 cos(B - C) - 2 cos A,
                               = cos A + 6 cos B cos C : cos B + 6 cos C cos A : cos C + 6 cos A cos B

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(546) lies on the Euler line. (Antreas Hatzipolakis, 1/20/00, Hyacinthos #201)

Let MA denote the point in which the A-median meets side BC. On 11/05/03, Andrew Crane noted that X(546) is the radical center of circles (A), (B), (C), where (A) denotes the circle centered at A and passing through MA, and (B) and (C) are defined cyclically.

X(546) lies on these lines: 2,3    13,398    14,397    113,137    156,578    946,952

X(546) = midpoint of X(I) and X(J) for these (I,J): (4,5), (382,550)
X(546) = reflection of X(I) in X(J) for these (I,J): (140,5), (548,140)
X(546) = inverse-in-orthocentroidal-circle of X(382)
X(546) = complement of X(550)

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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