## X(850) (BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA)

 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.

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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)/a3 : (c2 - a2)/b3 : (a2 - b2)/c3
Barycentrics    (b2 - c2)/a2 : (c2 - a2)/b2 : (a2 - b2)/c2

The barycentric product of X(850) and the circumcircle is the Kiepert hyperbola.

X(850) lies on these lines: 2,647    99,476    110,685    297,525    316,512    325,523    340,520    669,804    670,892

X(850) = isotomic conjugate of X(110)
X(850) = anticomplement of X(647)
X(850) = X(I)-Ceva conjugate of X(J) for these (I,J): (76,338), (99,311), (264,339)
X(850) = X(I)-cross conjugate of X(J) for these (I,J): (115,1502), (125,2), (338,76), (339,264)
X(850) = crosspoint of X(95) and X(99)
X(850) = crosssum of X(I) and X(J) for these (I,J): (32,669), (39,647), (51,512)
X(850) = crossdifference of any two points on line X(32)X(184)

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