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

X(1015)
(EXSIMILICENTER OF MOSES CIRCLE AND INCIRCLE)


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            a(b - c)2 : b(c - a)2 : c(a - b)2
Barycentrics    a2(b - c)2 : b2(c - a)2 : c2(a - b)2

The circle having center X(39) and radius 2R sin2ω, where R denotes the circumradius of triangle ABC, is here introduced as the Moses circle. It is tangent to the nine-point circle at X(115), and its internal and external centers of similitude with the incircle are X(1500) and X(1015), respectively. (Peter J. C. Moses, 5/29/03)

X(1015) lies on these lines:
1,39    2,668    6,101    11,115    32,56    36,187    37,537    55,574    76,330    214,1100    216,1060    244,665    350,538    812,1086

X(1015) = midpoint of X(1) and X(291)
X(1015) = isogonal conjugate of X(1016)
X(1015) = complement of X(668)
X(1015) = crosspoint of X(2) and X(513)
X(1015) = crosssum of X(I) and X(J) for these (I,J): (1,1018), (2,190), (6,100), (8,644), (101,595), (345,1332)
X(1015) = crossdifference of any two points on line X(100)X(190)

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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