## X(1489) (3RD STEVANOVIC POINT)

 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) = (csc A)[1 - cos(A/2) - sin(A/2)]
Barycentrics    1 - cos(A/2) - sin(A/2) : 1 - cos(B/2) - sin(B/2) : 1 - cos(C/2) - sin(C/2)

Let U be the A-excenter of triangle ABC; let A' be the incenter of triangle UBC, and define B', C' cyclically. Let I be the incenter of ABC, let A'' be the incenter of triangle IBC, and define B'', C'' cyclically. Let X = A'A''∩BC, and define Y, Z cyclically. Then AX, BY, CZ concur in X(1489). (Milorad R. Stevanovic, Hyacinthos #7185, 5/21/03. See also X(1130) and X(1489).)

X(1489) lies on these lines: 1,188    2,1143    174,558    258,483

X(1489) = complement of X(1143)
X(1489) = cevapoint of X(1) and X(258)
X(1489) = crosspoint of X(2) and X(1274)

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