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

X(1500)
(INSIMILICENTER 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 R tan ω sin 2ω, 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(1500) lies on these lines:
1,39    6,595    10,37    11,1508    12,115    32,55    35,172    41,1017    42,213    56,574    76,192    216,1062    346,941    519,1107    612,1196    756,762    1124,1505    1335,1504

X(1500) = isogonal conjugate of X(1509)
X(1500) = X(I)-Ceva conjugate of X(J) for these (I,J): (37,756), (42,872), (1018,512)
X(1500) = X(872)-cross conjugate of X(181)
X(1500) = crosspoint of X(37) and X(42)
X(1500) = crosssum of X(81) and X(86)

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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