X(46) = X(46) X(4)-CEVA CONJUGATE OF X(1)¶

Trilinears

\(cos B + cos C - cos A : :\)

\(a^3 + a^2(b + c) - a(b^2 + c^2) - (b - c)^2(b + c) : :\)

\(ra - R : :, where ra, rb, rc are the exradii\)

Barycentrics

\(a(cos B + cos C - cos A) : :\)

Notes

Let Ja’ be the reflection of the A-excenter in BC, and define Jb’, Jc’ cyclically. Let Oa be the circumcenter of AJb’Jc’, and define Ob, Oc cyclically. OaObOc and ABC are perspective at X(46). (Randy Hutson, July 20, 2016)

Let A’ be the inverse-in-Bevan-circle of the A-vertex of the hexyl triangle, and define B’ and C’ cyclically. The lines AA’, BB’, CC’ concur in X(46). (Randy Hutson, July 20, 2016)

Let JaJbJc be the excentral triangle. Let A″ be the inverse-in-Bevan-circle of A, and define B″, C″ cyclically. The lines JaA″, JbB″, JcC″ concur in X(46). (Randy Hutson, July 20, 2016)

X(46) lies on these lines: 1,3 4,90 9,79 10,63 19,579 34,47 43,851 58,998 78,758 80,84 100,224 158,412 169,672 200,1004 218,910 222,227 225,254 226,498 269,1103 404,997 474,960 499,946 595,614 750,975 978,1054

X(46) is the {X(3),:ref:X(65) <X(65)>}-harmonic conjugate of X(1). For a list of other harmonic conjugates of X(46), click Tables at the top of this page.

X(46) = reflection of X(i) in X(j) for these (i,j): (1,56), (1479,1210)

X(46) = isogonal conjugate of X(90)

X(46) = isotomic conjugate of X(20570)

X(46) = circumcircle-inverse of X(32760)

X(46) = Bevan-circle-inverse of X(36)

X(46) = X(4)-Ceva conjugate of X(1)

X(46) = crosssum of X(3) and X(1069)

X(46) = X(i)-aleph conjugate of X(j) for these (i,j): (4,46), (174,223), (188,1079), (366,610), (653, 1020)

X(46) = X(100)-beth conjugate of X(46)

X(46) = perspector of excentral and orthic triangles

X(46) = orthic isogonal conjugate of X(1)

X(46) = excentral isogonal conjugate of X(1490)