X(1581) (ISOGONAL CONJUGATE OF X(1580))

 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) = 1/(a4 - b2c2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1581) lies on these lines:
10,257    37,256    65,291    82,662    171,292    733,831    759,805    876,882

X(1581) = isogonal conjugate of X(1580)
X(1581) = isotomic conjugate of X(1966)
X(1581) = cevapoint of X(I) and X(J) for these (I,J): (1755,1964), (1965,1966)
X(1581) = X(I)-cross conjugate of X(J) for these (I,J): (1821,1956), (1959,1), (2227,75)

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