## X(239) (X(1)-LINE CONJUGATE OF X(42))

 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!

This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           bc(a2 - bc) : ca(b2 - ca) : ab(c2 - ab)
Barycentrics    a2 - bc : b2 - ca : c2 - ab

X(239) lies on these lines:
1,2    6,75    7,193    9,192    44,190    57,330    63,194    81,274    83,213    86,1100    92,607    141,319    238,740    241,664    257,333    294,666    318,458    320,524    335,518    514,649    1043,1104

X(239) = reflection of X(I) in X(J) for these (I,J): (190,44), (320,1086)
X(239) = isogonal conjugate of X(292)
X(239) = isotomic conjugate of X(335) X(239) = crosspoint of X(256) and X(291)
X(239) = crosssum of X(I) and X(J) for these (I,J): (3,255), (212,219)
X(239) = crossdifference of any two points on line X(42)X(649)
X(239) = X(I)-Hirst inverse of X(J) for these (I,J): (171,238), (665,1015)
X(239) = X(1)-line conjugate of X(42)
X(239) = X(I)-beth conjugate of X(J) for these (I,J): (333,239), (645,44)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.