## X(114) (KIEPERT ANTIPODE)

 Interactive Applet

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 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[b sec(B + ω) + c sec(C + ω)]
= cos(B - C) cos 2ω - sin ω sin(A + ω) (Peter J. C. Moses, 9/12/03)

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = b sec(B + ω) + c sec(C + ω)

X(114) = nine-point-circle-antipode of X(115)
X(114) = X(98)-of-medial triangle
X(114) = X(103)-of-orthic triangle.

X(114) lies on these lines:
2,98    3,127    4,99    5,39    25,135    52,211    113,690    132,684    136,427    325,511    381,543

X(114) = isogonal conjugate of X(2065)
X(114) = midpoint of X(I) and X(J) for these (I,J): (4,99), (98,147)
X(114) = reflection of X(I) in X(J) for these (I,J): (3,620), (115,5)
X(114) = complementary conjugate of X(511)
X(114) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,230), (4,511)
X(114) = crosspoint of X(2) and X(325)
X(114) = orthojoin of X(230)

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