## X(99) (STEINER POINT)

 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           bc/(b2 - c2) : ca/(c2 - a2) : ab/(a2 - b2)
= b2c2 csc(B - C) : c2a2 csc(C - A) : a2b2 csc(A - B)

Barycentrics    1/(b2 - c2) : 1/(c2 - a2) : 1/(a2 - b2)

X(99) = circumcircle-antipode of X(98)
X(99) = the point of intersection, other than A, B, and C, of the circumcircle and Steiner ellipse. X(99) = Ψ(X(6), X(2))

X(99) lies on these lines:
1,741    2,111    3,76    4,114    6,729    13,303    14,302    20,147    21,105    22,305    30,316    31,715    32,194    36,350    38,745    39,83    58,727    69,74    75,261    81,739    86,106    95,311    100,668    101,190    102,332    103,1043    104,314    108,811    109,643    110,690    112,648    141,755    163,825    187,385    249,525    264,378    286,915    298,531    299,530    310,675    476,850    512,805    523,691    524,843    666,919    669,886    670,804    692,785    695,711    813,1016    889,898

X(99) is the {X(39),X(384)}-harmonic conjugate of X(83).

X(99) = midpoint of X(I) and X(J) for these (I,J): (20,147), (616,617)
X(99) = reflection of X(I) in X(J) for these (I,J): (4,114), (13,619), (14,618), (98,3), (115,620), (148,115), (316,325), (385,187), (671,2)

X(99) = isogonal conjugate of X(512)
X(99) = isotomic conjugate of X(523)
X(99) = complement of X(148)
X(99) = anticomplement of X(115)
X(99) = cevapoint of X(I) and X(J) for these (I,J): (2,523), (3,525), (39,512), (100,190)
X(99) = X(1019)-cross conjugate of X(1509)
X(99) = crossdifference of any two points on line X(351)X(865)
X(99) = X(I)-cross conjugate of X(J) for these (I,J): (3,249), (22,250), (512,83), (523,2), (525,76)
X(99) = X(21)-beth conjugate of X(741)

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