## X(78) (ISOGONAL CONJUGATE OF X(34))

 Interactive Applet

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Download all construction files and macros: tc.zip (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/(1 - sec A) : 1/(1 - sec B) : 1/(1 - sec C)
= cos A csc2(A/2) : cos B csc2(B/2) : cos C csc2(C/2)
= (b + c - a)(b2 + c2 - a2) : (c + a - b)(c2 + a2 - b2) : (a + b - c)(a2 + b2 - c2)

Barycentrics    a/(1 - sec A) : b/(1 - sec B) : c/(1 - sec C)

X(78) lies on these lines:
1,2    3,63    4,908    9,21    20,329    29,33    37,965    38,988    40,100    46,758    55,960    56,480    57,404    69,73    101,205    207,653    210,958    212,283    220,949    226,377    271,394    273,322    280,282    345,1040    392,1057    474,942    517,945    644,728    999,1059

X(78) = isogonal conjugate of X(34)
X(78) = isotomic conjugate of X(273)
X(78) = X(I)-Ceva conjugate of X(J) for these (I,J): (69,63), (312,9), (332,345)
X(78) = X(I)-cross conjugate of X(J) for these (I,J): (3,271), (72,8), (212,9), (219,63)
X(78) = crosspoint of X(69) and X(345)
X(78) = crosssum of X(I) and X(J) for these (I,J): (25,608), (56,1406), (604,1395), (1042,1426)
X(78) = X(I)-beth conjugate of X(J) for these (I,J): (78,3), (643,40), (1043,1)

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

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense