## X(72) (ISOGONAL CONJUGATE OF X(28))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (b + c) cot A : (c + a) cot B : (a + b) cot C
= (b + c)(b2 + c2 - a2) : (c + a)(c2 + a2 - b2) : (a + b)(a2 + b2 - c2)

Barycentrics    (b + c) cos A : (c + a) cos B : (a + b) cos C

X(72) lies on these lines:
1,6    2,942    3,63    4,8    5,908    7,443    10,12    20,144    21,943    31,976    35,191    40,64    43,986    54,1006    56,997    57,474    69,304    73,201    74,100    145,452    171,1046    185,916    190,1043    222,1038    248,293    290,668    295,337    306,440    394,1060    519,950    672,1009    894,1010    940,975    978,982

X(72) is the {X(1),X(9)}-harmonic conjugate of X(405).

X(72) = reflection of X(I) in X(J) for these (I,J): (1,960), (65,10)
X(72) = isogonal conjugate of X(28)
X(72) = isotomic conjugate of X(286)
X(72) = anticomplement of X(942)
X(72) = X(I)-Ceva conjugate of X(J) for these (I,J): (8,10), (63,71), (69,306), (321,37)
X(72) = X(I)-cross conjugate of X(J) for these (I,J): (201,10), (228,37)
X(72) = crosspoint of X(I) and X(J) for these (I,J): (8,78), (63,69), (306,307)
X(72) = crosssum of X(I) and X(J) for these (I,J): (19,25), (34,56)
X(72) = crossdifference of any two points on line X(513)X(1430)
X(72) = X(I)-beth conjugate of X(J) for these (I,J): (8,65), (72,73), (78,72), (100,227), (644,72)

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