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

X(177)
(1ST MID-ARC POINT)


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 B/2 + cos C/2) sec A/2 : (cos C/2 + cos A/2) sec B/2 : (cos A/2 + cos B/2) sec C/2
Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)(cos B/2 + cos C/2) sec A/2

Let A',B',C' be the first points of intersection of the angle bisectors of ABC with its incircle. The tangents at A', B', C' form a triangle A"B"C", and the lines AA",BB",CC" concur in X(177). Also, X(177) = X(1) of the intouch triangle.

Clark Kimberling and G. R. Veldkamp, Problem 1160 and Solution, Crux Mathematicorum 13 (1987) 298-299 [proposed 1986].

X(177) is the perspector of ABC and the Yff central triangle, and X(177) is X(65)-of-the-Yff-central-triangle . (Darij Grinberg, Hyacinthos #7689, 8/25/2003)

X(177) lies on these lines: 1,167    7,555    8,556    9,173    57,164

X(177) = isogonal conjugate of X(260)
X(177) = X(7)-Ceva conjugate of X(234)
X(177) = crosspoint of X(7) and X(174)
X(177) = crosssum of X(55) and X(259)

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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