## X(952) (INTERSECTION OF X(1)X(5) AND X(3)X(8))

 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[2a4 - 2a3(b + c) - a2(b2 - 4bc + c2) + (2a - b - c)(b - c)(b2 - c2)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

As the isogonal conjugate of a point on the circumcircle, X(952) lies on the line at infinity.

X(952) lies on these lines:
1,5    3,8    4,145    10,140    30,511    40,550    150,664    182,996    390,1000    546,946    547,551    572,594

X(952) = isogonal conjugate of X(953)
X(952) = crossdifference of any two points on line X(6)X(654)

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