X(278) (ISOGONAL CONJUGATE OF X(219))

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

Barycentrics    tan A tan A/2 : tan B tan B/2 : tan C tan C/2

= 1 - sec A : 1 - sec B : 1 - sec C

X(278) lies on these lines:
1,4    2,92    7,27    19,57    25,105    28,56    65,387    88,653    109,917    219,329    240,982    241,277    242,459    274,331    354,955    393,1108    412,962    443,1038    614,1096

X(278) = isogonal conjugate of X(219)
X(278) = isotomic conjugate of X(345)
X(278) = X(I)-Ceva conjugate of X(J) for these (I,J): (27,57), (92,196), (273,4), (331,7)
X(278) = cevapoint of X(19) and X(34)
X(278) = X(I)-cross conjugate of X(J) for these (I,J): (19,4), (56,7), (225,273)

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