## X(141) (COMPLEMENT OF SYMMEDIAN POINT)

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           bc(b2 + c2) : ca(c2 + a2) : ab(a2 + b2)
= csc2A sin(A + ω) : csc2B sin(B + ω) : csc2C sin(C + ω)

Barycentrics    b2 + c2 : c2 + a2 : a2 + b2

X(141) = X(6)-of-medial triangle

X(141) lies on these lines:
2,6    3,66    5,211    10,142    37,742    39,732    45,344    53,264    67,110    75,334    76,698    95,287    99,755    113,127    116,121    125,126    140,182    239,319    241,307    308,670    311,338    317,458    320,894    384,1031    441,577    498,611    499,613    523,882    542,549    575,629    997,1060

X(141) is the {X(2),X(69)}-harmonic conjugate of X(6).

X(141) = midpoint of X(I) and X(J) for these (I,J): (6,69), (66,159), (67,110)
X(141) = reflection of X(I) in X(J) for these (I,J): (182,140), (597,2), (1353,575), (1386,1125)
X(141) = isogonal conjugate of X(251)
X(141) = isotomic conjugate of X(83)
X(141) = inverse-in-nine-point-circle of X(625)
X(141) = complement of X(6)
X(141) = complementary conjugate of X(2)
X(141) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,39), (67,524), (110,525)
X(141) = X(39)-cross conjugate of X(427)
X(141) = crosspoint of X(2) and X(76)
X(141) = crosssum of X(6) and X(32)
X(141) = X(39)-Hirst inverse of X(732)
X(141) = X(645)-beth conjugate of X(141)

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