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

Trilinears

\(tan B + tan C : :\)

\(a2(b2 + c2 - a2) ::\)

\(SBSC - S2 : SCSA - S2 : SASB - S2\)

\(1 - cot B cot C : :\)

\(sin 2A : :\)

Notes

Let A’B’C’ be the hexyl triangle. Let A″ be the barycentric product of the circumcircle intercepts of line B’C’. Define B″, C″ cyclically. The lines AA″, BB″, CC″ concur in X(48). (Randy Hutson, July 31 2018)

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),:ref:X(604) <X(604)>}-harmonic conjugate of X(6). For a list of other harmonic conjugates of X(48), click Tables at the top of this page.

X(48) = isogonal conjugate of X(92)

X(48) = isotomic conjugate of X(1969)

X(48) = complement of X(21270)

X(48) = anticomplement of X(20305)

X(48) = X(i)-Ceva conjugate of X(j) for these (i,j): (1,31), (2,36033), (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 every pair of 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)

X(48) = barycentric product of PU(16)

X(48) = vertex conjugate of PU(18)

X(48) = bicentric sum of PU(22)

X(48) = PU(22)-harmonic conjugate of X(656)

X(48) = trilinear pole of line X(810)X(822)

X(48) = X(2)-isoconjugate of X(4)

X(48) = X(75)-isoconjugate of X(19)

X(48) = X(91)-isoconjugate of X(1748)

X(48) = perspector of ABC and extraversion triangle of X(48) (which is also the anticevian triangle of X(48))

X(48) = crosspoint of X(2066) and X(5414)

X(48) = {X(1),:ref:X(19) <X(19)>}-harmonic conjugate of X(1953)

X(48) = perspector of circumconic centered at X(36033)