## X(222) (X(7)-CEVA CONJUGATE OF X(56))

 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           cos A tan A/2 : cos B tan B/2 : cos C tan C/2
= 1/(csc A + 2 csc 2A) : 1/(csc B + 2 csc 2B) : 1/(csc A + 2 csc 2C)
= a(b2 + c2 - a2)/(b + c - a) : b(c2 + a2 - b2)/(c + a - b) : c(a2 + b2 - c2)/(a + b - c)

Barycentrics    a2/(1 + sec A) : b2/(1 + sec B) : c2/(1 + sec C)

X(222) lies on these lines:
1,84    2,651    3,73    6,57    7,27    33,971    34,942    46,227    55,103    56,58    63,77    72,1038    171,611    189,281    218,241    226,478    268,1073    581,1035    601,1066    613,982    912,1060    1355,1363

X(222) = isogonal conjugate of X(281)
X(222) = X(I)-Ceva conjugate of X(J) for these (I,J): (7,56), (77,3), (81,57)
X(222) = cevapoint of X(6) and X(221)
X(222) = X(I)-cross conjugate of X(J) for these (I,J): (48,3), (73,77)
X(222) = crosspoint of X(7) and X(348)
X(222) = crosssum of X(I) and X(J) for these (I,J): (55,607), (650,1146)

X(222) = X(I)-beth conjugate of X(J) for these (I,J):
(21,1012), (63,63), (110,222), (287,222), (648,222), (651,222), (662,2), (895,222)

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