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

X(2003)
(ORTHOCORRESPONDENT OF X(36))


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) = yz + (-x cos A + y cos B + z cos C)x, where x : y : z = X(36)
Trilinears            sin(3A/2) sec(A/2) : sin(3B/2) sec(B/2) : sin(3C/2) sec(C/2)      (M. Iliev, 4/12/07)
Trilinears            (sin A + sin 2A)/(1 + cos A) : (sin B + sin 2B)/(1 + cos B) : (sin C + sin 2C)/(1 + cos C)      (M. Iliev, 4/12/07)
Trilinears            (1 + 2 cos A) tan(A/2) : (1 + 2 cos B) tan(B/2) : (1 + 2 cos C) tan(C/2)      (M. Iliev, 4/12/07) Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a(b2 + c2 - a2 + bc)/(b + c - a)       (M. Iliev, 5/13/07)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2003) lies on these lines:
1,90    6,57    9,394    35,500    42,109    56,1203    58,73    63,1993    65,267    77,1708    81,226    84,1181    212,991    255,581    323,1442    354,1421    386,603    648,1947    894,1943    1171,1400    1397,1469    1401,1428

X(2003) = X(1442)-Ceva conjugate of X(35)

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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