X(47) = X(110)-BETH CONJUGATE OF X(34)

Trilinears

\(cos 2A : cos 2B : cos 2C = f(a,b,c) : f(b,c,a) : f(c,a,b), where\)

\(a2 - 2R2 : b2 - 2R2 : c2 - 2R2\)

\(tan A cot 2A : :\)

\(cos^2 A - sin^2 A : :\)

\(1 - 2 sin^2 A : :\)

\(1 - 2 cos^2 A : :\)

Barycentrics

\(a cos 2A : b cos 2B : c cos 2C\)

Notes

Let A’B’C’ be the Kosnita triangle. Let A″ be the trilinear product B’*C’, and define B″, C″ cyclically. The lines AA″, BB″, CC″ concur in X(47). (Randy Hutson, March 21, 2019)

Let A’B’C’ and A″B″C″ be the Lucas and Lucas(-1) tangents triangles. Let A* be the trilinear product A’A″, and define B, C* cyclically. The lines AA*, BB*, CC* concur in X(47). (Randy Hutson, March 21, 2019)

X(47) lies on these lines: 1,21 19,921 33,90 34,46 35,212 36,602 91,92 158,162 171,498 238,499

X(47) is the {X(91),:ref:X(92) <X(92)>}-harmonic conjugate of X(564). For a list of other harmonic conjugates of X(47), click Tables at the top of this page.

X(47) = isogonal conjugate of X(91)

X(47) = isotomic conjugate of X(20571)

X(47) = anticomplement of X(34825)

X(47) = trilinear product X(371)

X(47) = X(92)-isoconjugate of X(1820)

X(47) = perspector of ABC and extraversion triangle of X(47) (which is also the anticevian triangle of X(47))

X(47) = eigencenter of cevian triangle of X(92)

X(47) = eigencenter of anticevian triangle of X(48)

X(47) = X(92)-Ceva conjugate of X(48)

X(47) = crosssum of X(i) and X(j) for these (i,j): (656,1109)

X(47) = X(275)-aleph conjugate of X(92)

X(47) = X(i)-beth conjugate of X(j) for these (i,j): (110,34), (643,47)

X(47) = trilinear product of X(371) and X(372)