## X(190) (YFF PARABOLIC POINT)

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           bc/(b - c) : ca/(c - a) : ab/(a - b)
Barycentrics    1/(b - c) : 1/(c - a) : 1/(a - b)

In unpublished notes, Yff has studied the parabola tangent to sidelines BC, CA, AB and having focus X(101). If A',B',C' are the respective points of tangency, then the lines AA', BB', CC' concur in X(190).

X(190) lies on these lines:
1,537    2,45    6,192    7,344    8,528    9,75    10,671    37,86    40,341    44,239    63,312    69,144    71,290    72,1043    99,101    100,659    110,835    162,643    191,1089    238,726    320,527    321,333    329,345    350,672    513,660    514,1016    522,666    644,651    646,668    649,889    658,1020    670,799    789,813    872,1045

X(190) = reflection of X(I) in X(J) for these (I,J): (239,44), (335,37), (673,9), (903,2)
X(190) = isogonal conjugate of X(649)
X(190) = isotomic conjugate of X(514)
X(190) = anticomplement of X(1086)
X(190) = X(99)-Ceva conjugate of X(100)
X(190) = cevapoint of X(I) and X(J) for these (I,J): (2,514), (9,522), (37,513), (440,525)
X(190) = X(I)-cross conjugate of X(J) for these (I,J): (513,86), (514,2), (522,75)
X(190) = crosssum of X(512) and X(798)
X(190) = X(I)-aleph conjugate of X(J) for these (I,J): (2,1052), (190,1), (645,411), (668,63), (1016,100)
X(190) = X(I)-beth conjugate of X(J) for these (I,J): (9,292), (190,651), (333,88), (645,190), (646,646), (1016,190)
X(190) = pole of the line X(1)X(2)

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