## X(1958) (CROSSSUM OF PU(23))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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) = cot2A + cot B cot C
Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a4 - a2b2 - a2c2 + 2b2c2       (M. Iliev, 5/13/07)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1958) lies on these lines:
19,326    31,1582    41,894    48,75    63,610    100,1253    239,604

X(1958) = X(I)-Ceva conjugate of X(J) for these (I,J): (293,1959), (775,63)
X(1958) = cevapoint of X(610) and X(1740)

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