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

X(1123)
(PAASCHE 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           1/(1 + sin A) : 1/(1 + sin B) : 1/(1 + sin C)
Barycentrics    (sin A)/(1 + sin A) : (sin B)/(1 + sin B) : (sin C)/(1 + sin C)

Let D and E be the congruent circles each tangent to the other and to line BC, with D also tangent to line AB and E also tangent to one CA, meeting in a point A' lying outside triangle ABC. Define B' and C' cyclically. Then A'B'C' is perspective to ABC, and the perspector is X(1123). See

Ivan Paasche, Aufgabe P 933, Praxis der Mathematik 1 (1990), page 40.

X(1123) lies on these lines: 2,586    37,158    57,482

X(1123) = isogonal conjugate of X(1124)
X(1123) = isotomic conjugate of X(1267)

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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