## X(1158) (CIRCUMCENTER OF EXTOUCH TRIANGLE)

 Interactive Applet

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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) = a6 - b6 - c6 + b2c2(b2 + c2) + 3a2(b4 + c4 - a2b2 - a2c2) + 2abc(a3 - b3 - c3 - abc + (a2 + bc)(b + c) - ab2 - ac2)

Trilinears           g(A,B,C) : g(B,C,A) : g(C,A,B),
where g(A,B,C) = sin2B/2 cos B + sin2C/2 cos C - sin2A/2 cos A (D. Grinberg, 2/25/04)

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

X(1158) = midpoint of X(40) and X(84)
X(1158) = X(3)-of-extouch triangle, so that X(210)X(1158) = Euler line of the extouch triangle

X(1158) lies on these lines:
1,104    3,960    4,46    8,20    57,946    65,1012    117,208    165,191

X(1158) = X(318)-Ceva conjugate of X(1)

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