X(76) (3RD BROCARD POINT)

 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           1/a3 : 1/b3 : 1/c3
= csc(A - ω) : csc(B - ω) : csc(C - ω)

Barycentrics    1/a2 : 1/b2 : 1/c2

X(76) lies on these lines:
1,350    2,39    3,98    4,69    5,262    6,83    8,668    10,75    13,299    14,298    17,303    18,302    31,734    32,384    85,226    95,96    100,767    115,626    141,698    275,276    297,343    321,561    335,871    338,599    485,491    486,492    524,598    689,755    693,764    761,789    826,882

X(76) is the {X(2),X(194)}-harmonic conjugate of X(39).

X(76) = reflection of X(194) in X(39)
X(76) = isogonal conjugate of X(32)
X(76) = isotomic conjugate of X(6)
X(76) = complement of X(194)
X(76) = anticomplement of X(39)
X(76) = X(I)-Ceva conjugate of X(J) for these (I,J): (308,2), (310,75)
X(76) = cevapoint of X(I) and X(J) for these (I,J): (2,69), (6,22), (75,312), (311,343), (313,321), (339,525)
X(76) = X(I)-cross conjugate of X(J) for these (I,J): (2,264), (69,305), (141,2), (321,75), (343,69), (525,99)
X(76) = crosssum of X(669) and X(1084)
X(76) = crossdifference of any two points on line X(669)X(688)
X(76) = X(I)-beth conjugate of X(J) for these (I,J): (76,85), (799,348)

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