## X(113) (JERABEK ANTIPODE)

 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) = sin B sin C [(sin C)/(cos C - 2 cos A cos B) + (sin B)/(cos B - 2 cos A cos C)]

Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where
g(A,B,C) = (sin C)/(cos C - 2 cos A cos B) + (sin B)/(cos B - 2 cos A cos C)

= h(a,b,c) : h(b,c,a) : h(c,a,b),
where h(a,b,c) = b2/(b2SB - 2SASC) + c2/(c2SC - 2SASB),
SA = (b2 + c2 - a2)/2, and SB and SC are defined cyclically (Peter J. C. Moses, 3/2003)

X(113) = nine-point-circle-antipode of of X(125)
X(113) = X(74)-of-medial triangle
X(113) = X(104)-of-orthic triangle

X(113) lies on these lines:
2,74    3,122    4,110    5,125    6,13    11,942    52,135    114,690    123,960    127,141    137,546

X(113) = midpoint of X(I) and X(J) for these (I,J): (4,110), (74,146), (265,399)
X(113) = reflection of X(I) in X(J) for these (I,J): (52,1112), (125,5)
X(113) = complementary conjugate of X(30)
X(113) = X(4)-Ceva conjugate of X(30)
X(113) = crosspoint of X(4) and X(403)
X(113) = crossdifference of any two points on line X(526)X(686)

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