## X(47) (X(110)-BETH CONJUGATE OF X(34))

 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           cos 2A : cos 2B : cos 2C = f(a,b,c) : f(b,c,a) : f(c,a,b), where
f(a,b,c) = a2(a4 + b4 + c4 - 2a2b2 - 2a2c2)

Barycentrics    a cos 2A : b cos 2B : c cos 2C

X(47) lies on these lines:
1,21    19,921    33,90    34,46    35,212    36,602    91,92    158,162    171,498    238,499

X(47) is the {X(91),X(92)}-harmonic conjugate of X(564).

X(47) = isogonal conjugate of X(91)
X(47) = eigencenter of cevian triangle of X(92)
X(47) = eigencenter of anticevian triangle of X(48)
X(47) = X(92)-Ceva conjugate of X(48)
X(47) = crosssum of X(I) and X(J) for these (I,J): (656,1109)
X(47) = X(275)-aleph conjugate of X(92)
X(47) = X(I)-beth conjugate of X(J) for these (I,J): (110,34), (643,47)
X(47) = trilinear product of X(371) and X(372)

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