## X(1843) (ZOSMA TRANSFORM OF X(75))

 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           (y + z) sec A : (z + x) sec B : (x + y) sec C,    x : y : z = X(75)
Barycentrics    (y + z) tan A : (z + x) tan B : (x + y) tan C,    x : y : z = X(75)

X(1843) lies on these lines:
4,69    6,25    24,182    34,1469    112,755    113,1596    125,1205    141,427    143,1353    155,1351    157,571    160,570    181,1395    185,1503    216,237    263,393    373,468    428,524    518,1829    674,1824    1350,1593    1827,1828

X(1843) = reflection of X(I) in X(J) for these (I,J): (1205,125), (1289,647)
X(1843) = isogonal conjugate of X(1799)
X(1843) = X(I)-Ceva conjugate for these (I,J): (4,427), (427,39), (1289,647)
X(1843) = crosspoint of X(I) and X(J) for these (I,J): (4,25), (6,66)
X(1843) = crosssum of X(I) and X(J) for these (I,J): (2,22), (3,69)

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