## X(1580) (POINT ALUDRA)

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

X(1580) lies on these lines:
1,21    6,256    41,43    75,560    87,604    171,172    238,1284    239,1281    284,1045    661,830    662,922

X(1580) = isogonal conjugate of X(1581)
X(1580) = isotomic conjugate of X(1934)
X(1580) = X(I)-Ceva conjugate of X(J) for these (I,J): (1755,1955), (1910,1), (1967,1582)
X(1580) = X(2236)-cross conjugate of X(1966)
X(1580) = crosssum of X(I) and X(J) for these (I,J): (1755,1964), (1965,1966)
X(1580) = crossdifference of any two points on line X(38)X(661)
X(1580) = X(98)-aleph conjugate of X(1755)

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