X(28) = CEVAPOINT OF X(19) AND X(25)

Trilinears

\((tan A)/(b + c) : (tan B)/(c + a) : (tan C)/(a + b)\)

Barycentrics

\((sin A tan A)/(b + c) : (sin B tan B)/(c + a) : (sin C tan C)/(a + b)\)

Notes

As a point on the Euler line, X(28) has Shinagawa coefficients ($a$F, -$a$(E + F) - abc).

If you have The Geometer’s Sketchpad, you can view X(28). If you have GeoGebra, you can view X(28).

X(28) is the {X(27),:ref:X(29) <X(29)>}-harmonic conjugate of X(4). For a list of other harmonic conjugates of X(28), click Tables at the top of this page.

X(28) = isogonal conjugate of X(72)

X(28) = isotomic conjugate of X(20336)

X(28) = anticomplement of X(21530)

X(28) = trilinear pole of line X(513)X(1430) (the polar of X(321) wrt polar circle)

X(28) = polar conjugate of X(321)

X(28) = X(6)-isoconjugate of X(306)

X(28) = X(75)-isoconjugate of X(228)

X(28) = circumcircle-inverse of X(2074)

X(28) = X(i)-Ceva conjugate of X(j) for these (i,j): (270,58), (286,81)

X(28) = cevapoint of X(i) and X(j) for these (i,j): (19,25), (34,56)

X(28) = X(i)-cross conjugate of X(j) for these (i,j): (19,27), (58,58)

X(28) = crossdifference of every pair of points on line X(647)X(656)

X(28) = X(4)-Hirst inverse of X(422)

X(28) = X(i)-beth conjugate of X(j) for these (i,j): (29,29), (107,28), (162,28), (270,28)