X(991) (INTERSECTION OF LINES X(1)X(7) AND X(3)X(6))

 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[a3(b + c) - a2(b2 - bc + c2) - a(b + c)(b2 + c2) + (b - c)(b3 - c3)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(991) lies on these lines:
1,7    3,6    35,255    37,971    42,165    55,103    57,955    995,1064

X(991) = reflection of X(573) in X(3)
X(991) = crossdifference of any two points on line X(523)X(657)

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