## X(2078) (INVERSE-IN-CIRCUMCIRCLE OF X(57))

 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) = r - 2R + 2(r + R) cos A
= g(A,B,C) : g(B,C,A) : g(C,A,B),
where g(A,B,C) = cos B + cos C - 3 + (1 + 2 cos A + 2 cos B + 2 cos C) cos A
Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a(a2 + b2 + c2 - 2ab - 2ac + bc)/(b+c-a)       (M. Iliev, 5/13/07)

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

X(2078) lies on these lines:
1,3    31,2003    59,672    73,595    105,2006    109,840    226,1005    388,535    581,1497    901,1477    1174,1202    1279,1421    1283,1284    1308,1323

X(2078) = inverse-in-circumcircle of X(57)
X(2078) = crosssum of X(142) and X(527)

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