## X(212) (X(9)-CEVA CONJUGATE OF X(41))

 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)(1 + cos A) : (cos B)(1 + cos B) : (cos C)(1 + cos C)
= (cos A)cos2(A/2) : (cos B)cos2(B/2) : (cos C)cos2(C/2)
= a2(b + c - a)(b2 + c2 - a2) : b2(c + a - b)(c2 + a2 - b2) : c2(a + b - c)(a2 + b2 - c2)

Barycentrics    (sin 2A)(1 + cos A) : (sin 2B)(1 + cos B) : (sin 2C)(1 + cos C)

X(212) lies on these lines:
1,201    3,73    6,31    9,33    11,748    34,40    35,47    48,184    56,939    63,1040    78,283    109,165    154,198    238,497    312,643    582,942

X(212) = isogonal conjugate of X(273)
X(212) = X(I)-Ceva conjugate of X(J) for these (I,J): (3,48), (9,41), (283,219)
X(212) = X(228)-cross conjugate of X(55)
X(212) = crosspoint of X(I) and X(J) for these (I,J): (3,219), (9,78)
X(212) = crosssum of X(I) and X(J) for these (I,J): (4,278), (34,57)
X(212) = X(212)-beth conjugate of X(184)

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