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

X(312)
(ISOTOMIC CONJUGATE OF X(57))


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.

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           (b + c - a)b2c2 : (c + a - b)c2a2 : (a + b - c)a2b2
                                    = (1 + cos A)csc(A - ω) : (1 + cos B)csc(B - ω) : (1 + cos C)csc(C - ω)

Trilinears           (csc A)/(1 - cos A) : (csc B)/(1 - cos B) : (csc C)/(1 - cos C)      (M. Iliev, 4/12/07)

Barycentrics    bc(b + c - a) : ca(c + a - b) : ab(a + b - c)

X(312) lies on these lines: 1,1089    2,37    8,210    9,314    29,33    63,190    69,189    76,85    92,264    212,643    223,664    726,982    894,940    975,1010

X(312) = isogonal conjugate of X(604)
X(312) = isotomic conjugate of X(57)
X(312) = complement of X(3210)
X(312) = X(I)-Ceva conjugate of X(J) for these (I,J): (76,75), (304,322), (314,8)
X(312) = cevapoint of X(I) and X(J) for these (I,J): (2,329), (8,346), (9,78), (306,321)
X(312) = X(I)-cross conjugate of X(J) for these (I,J): (8,75), (9,318), (306,345), (346,341)
X(312) = crosssum of X(I) and X(J) for these (I,J): (32,1397), (56,1403), (57,1424)

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



free counter