## X(1593) (POINT CEBALRAI)

 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) = cos A + sec A
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1593) lies on these lines:
1,1037    2,3    6,64    19,1212    33,56    34,55    51,1204    74,1112    84,1473    184,1498    208,1466    264,1105    578,1181    607,672    1155,1452    1208,1471

X(1593) = reflection of X(I) in X(J) for these (I,J): (4,1595), (1181,578)
X(1593) = inverse-in-orthocentroidal-circle of X(235)
X(1593) = crosspoint of X(4) and X(1595)
X(1593) = crosssum of X(3) and X(1181)

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