X(1826) (ZOSMA TRANSFORM OF X(6))

 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           (y + z) sec A : (z + x) sec B : (x + y) sec C,    x : y : z = X(6)
Barycentrics    (y + z) tan A : (z + x) tan B : (x + y) tan C,    x : y : z = X(6)

X(1826) lies on these lines:
4,9    6,1837    11,1108    12,37    25,1631    27,1268    28,1224    29,1220    33,42    48,515    53,1904    65,1868    80,1172    92,264    101,1300    209,1859    210,430    219,355    286,334    407,1213    427,1841    579,1737    608,1877    857,1441    1744,1770    1836,1853

X(1826) = isogonal conjugate of X(1790)
X(1826) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,1824), (281,37)
X(1826) = cevapoint of X(1) and X(1719)
X(1826) = X(42)-cross conjugate of X(10)
X(1826) = crosspoint of X(4) and X(92)
X(1826) = crosssum of X(3) and X(48)

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