## X(1384) (2ND GRINBERG HOMOTHETIC CENTER)

 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           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(b2 + c2 - 5a2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Let Ga be the circumcenter of triangle BCG, where G - centroid(ABC). Define Gb and Gc cyclically. Triangle GaGbGc is homothetic to the pedal triangle of X(6), and X(1384) is the center of the homothety.

X(1384) lies on these lines: 3,6    25,111    55,609    230,381    385,1003

X(1384) = X(1383)-Ceva conjugate of X(6)

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