## X(2501) (RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT CIRCLE, TAYLOR CIRCLE})

 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           (b2 - c2)sec A : (c2 - a2)sec B : (a2 - b2)sec C
Barycentrics    SBSC(SB - SC) : SCSA(SC - SA) : SASB(SA - SB)

X(2501) lies on these lines:
4,1499    25,669    107,685    112,476    230,231    297,525    393,2433    421,2623    450,2451    460,512    648,892

X(2501) = X(I)-Ceva conjugate of X(J) for these I,J: 2,136    92,2969    107,25    112,53    264,2971    393,115    648,4    653,407    685,460    687,30    1783,1865    1897,430    2052,2970

X(2501) = cevapoint of X(I) and X(J) for these I,J: 6,2079    512,2489
X(2501) = X(I)-Ceva conjugate of X(J) for these I,J: 115,393    512,523    2971,264
X(2501) = crosspoint of X(I) and X(J) for these I,J: 2,925    4,648    107,2052
X(2501) = crosssum of X(I) and X(J) for these I,J: 3,647    6,924    343,525    520,577    906,1331

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