## X(34) (X(4)-BETH CONJUGATE OF X(4))

 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           1 - sec A : 1 - sec B : 1 - sec C
= tan A tan(A/2) : tan B tan(B/2) : tan C tan(C/2)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[(b + c - a)(b2 + c2 - a2)]
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sec A sin2(A/2)

Barycentrics    sin A - tan A : sin B - tan B : sin C - tan C
= h(A,B,C) : h(B,C,A) : h(C,A,B), where h(A,B,C) = tan A sin2(A/2)

X(34) is the center of perspective of the orthic triangle and the reflection in the incenter of the intangents triangle.

X(34) lies on these lines:
1,4    2,1038    5,1060    6,19    7,1039    8,1041    9,201    10,475    11,235    12,427    20,1040    24,36    25,56    28,57    29,77    30,1062    35,378    40,212    46,47    55,227    79,1061    80,1063    87,242    106,108    196,937    207,1042    222,942    244,1106    331,870    347,452    860,997

X(34) is the {X(1),X(4)}-harmonic conjugate of X(33).

X(34) = isogonal conjugate of X(78)
X(34) = X(I)-Ceva conjugate of X(J) for these (I,J): (1,207), (4,208), (28,56), (273,57), (278,19)
X(34) = X(25)-cross conjugate of X(19)
X(34) = crosssum of X(219) and X(1260)
X(34) = X(56)-Hirst inverse of X(1430)
X(34) = X(I)-beth conjugate of X(J) for these (I,J):
(1,221), (4,4), (28,34), (29,1), (107,158), (108,34), (110,47), (162,34), (811,34)

X(34) = crossdifference of any two points on line X(521)X(652)

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