## X(69) (SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE)

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (cos A)/a2 : (cos B)/b2 : (cos C)/c2
= bc(b2 + c2 - a2) : ca(c2 + a2 - b2) : ab(a2 + b2 - c2)

Barycentrics    cot A : cot B : cot C
= b2 + c2 - a2 : c2 + a2 - b2 : a2 + b2 - c2

X(69) lies on these lines:
2,6    3,332    4,76    7,8    9,344    10,969    20,64    22,159    54,95    63,71    72,304    73,77    74,99    110,206    125,895    144,190    150,668    189,309    192,742    194,695    200,269    248,287    263,308    265,328    274,443    290,670    297,393    347,664    350,497    404,1014    478,651    485,639    486,640    520,879

X(69) is the {X(7),X(8)}-harmonic conjugate of X(75).

X(69) = reflection of X(I) in X(J) for these (I,J): (2,599), (4,1352), (6,141), (20,1350), (193,6), (895,125), (1351,5), (1353,140)

X(69) = isogonal conjugate of X(25)
X(69) = isotomic conjugate of X(4)
X(69) = cyclocevian conjugate of X(253)
X(69) = complement of X(193)
X(69) = anticomplement of X(6)
X(69) = anticomplementary conjugate of X(2)
X(69) = X(I)-Ceva conjugate of X(J) for these (I,J): (76,2), (304,345), (314,75), (332,326)
X(69) = cevapoint of X(I) and X(J) for these (I,J): (2,20), (3,394), (6,159), (8,329), (63,78), (72,306), (125,525)

X(69) = X(I)-cross conjugate of X(J) for these (I,J):
(3,2), (63,348), (72,63), (78,345), (125,525), (306,304), (307,75), (343,76)

X(69) = crosspoint of X(I) and X(J) for these (I,J): (76,305), (314,332)
X(69) = X(2)-Hirst inverse of X(325)
X(69) = X(I)-beth conjugate of X(J) for these (I,J): (69,77), (99,347), (314,7), (332,69), (645,69), (668,69)

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