HJB --- GMA --- UFF


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: (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) = a3 + a(bc - b2 - c2) - bc(b + c)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

The term "AC-incircle" is introduced for "anticomplement of the incircle" by Peter Moses (Dec. 2, 2004). Thus, the AC-incircle is the incircle of the anticomplementary triangle; the circle has center X(8) and radius 2r. The exsimilicenter of the circumcircle and AC-incircle is X(100), their touchpoint, and the anticomplement of X(11).

X(2975) lies on these lines:
1,21    2,12    3,8    9,604    10,36    20,2894    28,92    35,519    48,2287    54,72    55,145    75,1444    78,947    105,330    110,1098    144,1001    172,1107    198,391    229,409    238,1201    329,405    333,1610    348,934    411,515    518,2330    593,2363    596,759    668,1078    672,2329    908,1125    943,2320    950,1005    960,1319    962,1012    966,2178    995,1724    1457,1935    1470,1788    1478,2476    1761,1953    2475,2886

X(2975) = anticomplement of X(12)
X(2975) = X(I)-Ceva conjugate of X(J) for these I,J: 59,100    261,2
X(2975) = crosssum of X(512) and X(2170)

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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