## X(48) (CROSSPOINT OF X(1) AND X(63))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           sin 2A : sin 2B : sin 2C
= f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = tan B + tan C
= g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a2(b2 + c2 - a2)

Barycentrics    a sin 2A : b sin 2B : c sin 2C

X(48) lies on these lines:
1,19    3,71    6,41    9,101    31,560    36,579    37,205    42,197    55,154    63,326    75,336    163,1094    184,212    220,963    255,563    281,944    282,947    354,584    577,603    692,911    949,1037    958,965

X(48) is the {X(41),X(604)}-harmonic conjugate of X(6).

X(48) = isogonal conjugate of X(92)
X(48) = isotomic conjugate of X(1969)
X(48) = X(I)-Ceva conjugate of X(J) for these (I,J): (1,31), (3,212), (63,255), (92,47), (284,6)
X(48) = X(228)-cross conjugate of X(3)
X(48) = crosspoint of X(I) and X(J) for these (I,J): (1,63), (3,222), (91,92), (219,268)
X(48) = crosssum of X(I) and X(J) for these (I,J): (1,19), (4,281), (47,48), (196,278), (523,1146), (661,1109)
X(48) = crossdifference of any two points on line X(240)X(522)
X(48) = X(1)-line conjugate of X(240)
X(48) = X(I)-beth conjugate of X(J) for these (I,J): (101,48), (219,219), (284,604), (906,48)

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