## X(1837) (ZOSMA TRANSFORM OF X(34))

 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(34)
Barycentrics    (y + z) tan A : (z + x) tan B : (x + y) tan C,    x : y : z = X(34)

X(1837) lies on these lines:
1,5    3,1737    4,65    6,1826    8,210    10,55    19,1852    20,1155    30,46    33,429    40,1728    56,515    78,1329    221,1877    354,388    382,1770    499,1385    517,1479    942,1478    944,1319    1040,1722    1399,1771    1464,1745    1853,1854

X(1837) = midpoint of X(65) and X(1898)
X(1837) = reflection of X(I) in X(J) for these (I,J): (1,496), (56,1210), (78,1329)
X(1837) = inverse-in-Fuhrmann-circle of X(11)
X(1837) = crosspoint of X(4) and X(8)
X(1837) = crosssum of X(3) and X(56)

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