## X(1146) (CENTER OF HYPERBOLA {A,B,C,X(2),X(8)})

 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) = bc[(b - c)(b + c - a)]2
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Coordinates found by Paul Yiu (#4197, 10/24/01)

X(1146) lies on these lines:
2,664    6,281    8,220    9,80    101,952    115,124    116,514    169,355    515,910    918,1086

X(1146) = midpoint of X(2) and X(1121)
X(1146) = reflection of X(1565) in X(116)
X(1146) = isogonal conjugate of X(1262)
X(1146) = isotomic conjugate of X(1275)
X(1146) = complement of X(664)
X(1146) = crosspoint of X(I) and X(J) for these (I,J): (2,522), (4,514), (9,1021)
X(1146) = crosssum of X(I) and X(J) for these (I,J): (3,101), (6,109), (56,1415), (57,1020), (1407,1461)
X(1146) = crossdifference of any two points on line X(109)X(692)

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