## X(2594) (SUM OF PU(68))

 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) = cos(C- A) + cos(B - A)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

The notation "PU(68)", as described in the Bicentric Pairs section accessible by the More button, abbreviates a bicentric pair of points P = p : q : r and U = u : v : w, where p, q, r have the form g(a,b,c), g(b,c,a), g(c,a,b) and u,v,w have the form h(a,b,c), h(b,c,a), h(c,a,b). "Sum of PU(68)" denotes the point

g(a,b,c) + h(a,b,c) : g(b,c,a) + h(b,c,a) : g(c,a,b) + h(c,a,b),

where (P, Q) are the bicentric pair (P(68),Q(68)) as listed in the Bicentric Pairs section.

X(2594) lies on these lines:
1,5    6,2197    35,500    42,65    55,581    56,181    59,60    354,1066    523,2616    654,2598    995,1388    1048,2595    1193,1319    1203,2078    1324,1437    1745,1836    2151,2307    2601,2603

X(2594) = X(1)-Ceva conjugate of X(2599)
X(2594) = cevapoint of X(1) and X(1048)
X(2594) = crosspoint of X(1) and X(54)
X(2594) = crosssum of X(1) and X(5)

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