## X(1086) (CENTER OF HYPERBOLA {A,B,C,X(2),X(7)})

 Interactive Applet

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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)2
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = (b - c)2

The line f(a,b,c)x + f(b,c,a)y + f(c,a,b)z = 0 is tangent to the circumcircle at X(101). Also, X(1086) is the point of tangency of the Steiner inscribed ellipse with the line tangent to the nine-point circle and the incircle. (Paul Yiu, #4197, 11/24/01).

X(1086) lies on these lines:
1,528    2,45    6,7    8,599    10,537    11,244    37,142    44,527    53,273    57,1020    75,141    115,116    220,277    239,320    812,1015    918,1111

X(1086) = midpoint of X(I) and X(J) for these (I,J): (2,903), (7,673), (75,335), (239,320)
X(1086) = isogonal conjugate of X(1252)
X(1086) = isotomic conjugate of X(1016)
X(1086) = complement of X(190)
X(1086) = crosspoint of X(2) and X(514)
X(1086) = crosssum of X(I) and X(J) for these (I,J): (6,101), (9,1018), (32,692), (219,906)
X(1086) = crossdifference of any two points on line X(101)X(692)

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