## X(115) (CENTER OF KIEPERT HYPERBOLA)

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           bc(b2 - c2)2 : ca(c2 - a2)2 : ab(a2 - b2)2
= cos A - 2 cos(B - C) + cot ω sin A (Peter J. C. Moses, 9/12/03)

Barycentrics    (b2 - c2)2 : (c2 - a2)2 : (a2 - b2)2

X(115) lies on the nine-point circle
X(115) = X(99)-of-medial triangle
X(115) = X(101)-of-orthic triangle

Roland H. Eddy and R. Fritsch, "The conics of Ludwig Kiepert: a comprehensive lesson in the geometry of the triangle," Mathematics Magazine 67 (1994) 188-205.

X(115) lies on these lines:
2,99    4,32    5,39    6,13    11,1015    30,187    50,231    53,133    76,626    116,1086    120,442    125,245    127,338    128,233    129,389    131,216    232,403    316,385    325,538    395,530    396,531    593,1029    804,1084

X(115) = midpoint of X(I) and X(J) for these (I,J): (4,98), (13,14), (99,148), (316,385)
X(115) = reflection of X(I) in X(J) for these (I,J): (99,620), (114,5), (187,230), (325,625)
X(115) = isogonal conjugate of X(249)
X(115) = inverse-in-orthocentroidal-circle of X(6)
X(115) = complementary conjugate of X(512)
X(115) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,523), (4,512), (338,125)
X(115) = crosspoint of X(I) and X(J) for these (I,J): (2,523), (68,525)
X(115) = crosssum of X(I) and X(J) for these (I,J): (6,110), (24,112), (163,849)
X(115) = crossdifference of any two points on line X(110)X(351)
X(115) = X(2)-Hirst inverse of X(148)

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