X(1104) (CROSSPOINT OF X(1) AND X(28))

 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) = 2avw + cv2 + bw2 + u(bv + cw), u : v : w = X(72)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(1104) is the midpoint of the bicentric pair y : z : x and z : x : y, where x : y : z = X(72)

X(1104) lies on these lines:
1,6    11,429    25,34    31,65    32,910    58,942    81,1098    105,961    210,976    229,593    239,1043    440,950    517,580    581,995

X(1104) = isogonal conjugate of X(1257)
X(1104) = crosspoint of X(I) and X(J) for these (I,J): (1,28), (81,269)
X(1104) = crosssum of X(I) and X(J) for these (I,J): (1,72), (37,200)

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