## X(1490) (INTERSECTION OF LINES X(1)X(4) and X(3)X(9))

 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) = 1 + sec A - sec B - sec C
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1490) is the X(68)-of-the-excentral triangle and the circumcircle-antipode of X(84). These and other properties itemized here were reported by Darij Grinberg, May 19, 2003.

X(1490) lies on these lines:
1,4    3,9    20,78    40,64    63,411    165,191    224,908    386,990    910,1192    975,991    1045,1047    1210,1467

X(1490) = reflection of X(84) in X(3)
X(1490) = X(I)-Ceva conjugate of X(J) for these (I,J): (78,1), (329,9)
X(1490) = X(207)-cross conjugate of X(1)

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