## X(312) (ISOTOMIC CONJUGATE OF X(57))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (b + c - a)b2c2 : (c + a - b)c2a2 : (a + b - c)a2b2
= (1 + cos A)csc(A - ω) : (1 + cos B)csc(B - ω) : (1 + cos C)csc(C - ω)

Trilinears           (csc A)/(1 - cos A) : (csc B)/(1 - cos B) : (csc C)/(1 - cos C)      (M. Iliev, 4/12/07)

Barycentrics    bc(b + c - a) : ca(c + a - b) : ab(a + b - c)

X(312) lies on these lines: 1,1089    2,37    8,210    9,314    29,33    63,190    69,189    76,85    92,264    212,643    223,664    726,982    894,940    975,1010

X(312) = isogonal conjugate of X(604)
X(312) = isotomic conjugate of X(57)
X(312) = complement of X(3210)
X(312) = X(I)-Ceva conjugate of X(J) for these (I,J): (76,75), (304,322), (314,8)
X(312) = cevapoint of X(I) and X(J) for these (I,J): (2,329), (8,346), (9,78), (306,321)
X(312) = X(I)-cross conjugate of X(J) for these (I,J): (8,75), (9,318), (306,345), (346,341)
X(312) = crosssum of X(I) and X(J) for these (I,J): (32,1397), (56,1403), (57,1424)

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