## X(1145) (3RD EHRMANN POINT)

 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 , 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) = bc(b + c - 2a)[2abc - (b + c)(a2 - (b - c)2)]
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Let A',B',C' be the respective excenters of ABC, and let Ab be the projection of A on A'B', let Ac be the projection of A on A'C', and define Bc, Ba, Ca, Cb cyclically. The Euler lines of the three triangles A'AbAc, B'BcBa, C'CaCb concur in X(1145). Also, X(1145) is X(974) of the excentral triangle. (Analogously, X(442) is X(973) of the excentral triangle; see the note at X(442).) Jean-Pierre Ehrmann (#4200, 10/24/01)

X(1145) lies on these lines:
2,1000    3,8    9,80    10,11    119,517    144,153    214,519    484,529

X(1145) = midpoint of X(8) and X(100)
X(1145) = reflection of X(I) in X(J) for these (I,J): (11,10), (1317,214), (1320,1387), (1537,119)
X(1145) = anticomplement of X(1387)

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