## X(1154) (ISOGONAL CONJUGATE OF X(1141))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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) = a[16D2 + (a2+c2-b2)(a2+b2-c2)][16D2 - 3(b2+c2-a2)2],
where D = area(ABC).
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

As the isogonal conjugate of a point on the circumcircle, X(1154) lies on the line at infinity; X(1154) is, in fact, the point where the Euler line of the orthic triangle meets the line at infinity (Bernard Gibert, Hyacinthos 1498, September 25, 2000).

X(1154) lies on these lines:
2,568    3,54    4,93    5,51    26,154    30,511    35,500    140,389    185,550    186,323    403,1112

X(1154) = isogonal conjugate of X(1141)
X(1154) = complementary conjugate of X(128)
X(1154) = X(I)-Ceva conjugate of X(J) for these (I,J): (3,1511), (4,128)
X(1154) = crosspoint of X(I) and X(J) for these (I,J): (5,1263), (323,340)
X(1154) = crosssum of X(I) and X(J) for these (I,J): (3,539), (54,1157)

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