## X(1576) (ISOGONAL CONJUGATE OF X(850))

 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           a3/(b2 - c2) : b3/(c2 - a2) : c3/(a2 - b2)
Barycentrics    a4/(b2 - c2) : b4/(c2 - a2) : c4/(a2 - b2)

X(1576) is the perspector of the excentral triangle and the apices of equilateral triangles constructed outward from the sides, as in the construction of X(13). (Paul Yiu, 2/27/04).

X(1576) lies on these lines:
3,1177    6,157    32,1084    50,237    99,827    107,933    110,351    160,206    163,692    250,523    338,1316    662,1492

X(1576) = midpoint of X(648) and X(1632)
X(1576) = isogonal conjugate of X(850)
X(1576) = X(I)-Ceva conjugate of X(J) for these (I,J): (249,1501), (250,6), (827,110), (933,112)
X(1576) = cevapoint of X(I) and X(J) for these (I,J): (32,669), (39,647), (51,512)
X(1576) = X(I)-cross conjugate of X(J) for these (I,J): (669,32), (1501,249)
X(1576) = crosspoint of X(110) and X(112)
X(1576) = crosssum of X(523) and X(525)
X(1576) = crossdifference of any two points on line X(115)X(127)

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