## X(3022) (6th STEVANOVIC POINT)

 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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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            f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(b - c)2(b + c - a)3
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3022) lies on the incircle and these lines:
1,1362    11,116    12,118    33,181    56,103    65,1360    101,2291    150,497    152,388    926,2170    928,1364    950,2784    1282,1697    1317,2801    1359,2823    1361,2099    1397,2192    1682,3033    2772,3028    2774,3024    2786,3023    2809,3021

X(3022) = reflection of X(I) in X(J) for these I,J: 8,3041    1362,1
X(3022) = X(I)-Ceva conjugate of X(J) for these I,J: 7,650    55,657
X(3022) = crosspoint of X(I) and X(J) for these I,J: 7,650    55,657    607,663
X(3022) = crosssum of X(I) and X(J) for these I,J: 7,658    55,651    100,144    279,934    348,664

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