INSTITUTO DE MATEMÁTICA HJB --- GMA --- UFF

 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[3a4 - 2a3(b + c) + (b - c)2(2ab + 2ac - 2bc - b2 - c2 - 2a2)]
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 1 - cos A - cos B - cos C + cos B cos C

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(944) is the point in which the extended legs X(4)X(1) and X(3)X(8) of the trapezoid X(4)X(1)X(3)X(8) meet. The point is introduced in

Hofstadter, Douglas. R., "Discovery and dissection of a geometric gem," in Geometry Turned On! editors J. R. King and D. Schattschneider, Mathematical Association of America, Washington, D. C., 1997, 3-14.

The centroid of ABC is also the centroid of triangle X(4)X(8)X(944). (Darij Grinberg, August 22, 2002)

X(944) lies on these lines:
1,4    2,355    3,8    10,631    20,145    30,962    40,376    48,281    80,499    84,1000    150,348    390,971    392,452    938,999    958,1006

X(944) = midpoint of X(20) and X(145)
X(944) = reflection of X(I) in X(J) for these (I,J): (4,1), (8,3), (355,1385), (962,1482)
X(944) = isogonal conjugate of X(945)
X(944) = anticomplement of X(355)

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