## X(2999) (DANNEELS-BEVAN HOMOTHETIC CENTER)

 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.

 The JRE (Java Runtime Environment) is not enabled in your browser!

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) = (a + b + c)2 - 4bc
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Let RA be the radical axis of the Bevan circle and the A-excircle. Define RB and RC cyclically. The three radical axes form a triangle homothetic to triangle ABC, and X(2999) is the center of homothety. (Eric Danneels, Hyacinthos #10926, Dec. 5, 2004.

X(2999) lies on these lines:
1,2    3,1453    6,57    31,165    46,1203    58,937    63,1743    73,1467    244,1282    278,2331    440,1040    673,2258    748,968    940,1449    990,1750    1191,1697    1214,2257    1376,1386    1394,1466

X(2999) = isogonal conjugate of X(2297)
X(2999) = crosssum of X(9) and X(1449)

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