X(82) = ISOGONAL CONJUGATE OF X(38)¶

Trilinears

\(1/(b2 + c2) : 1/(c2 + a2) : 1/(a2 + b2)\)

\(sin A csc(A + ω) : sin B csc(B + ω) : sin C csc(C + ω) Barycentrics a/(b2 + c2) : b/(c2 + a2) : c/(a2 + b2) Let A'B'C' be the circummedial triangle. Let A″ be the trilinear product B'*C', and define B″, C″ cyclically. A″, B″, C″ are collinear on line :ref:`X(798) <X(798)>\)X(812) (the trilinear polar of X(3112)). The lines AA″, BB″, CC″ concur in X(82). (Randy Hutson, October 15, 2018) X(82) lies on these lines: 1,560 10,83 31,75 37,251 58,596 689,715 759,827 X(82) = isogonal conjugate of X(38) <X(38)>`

Barycentrics

\(a/(b2 + c2) : b/(c2 + a2) : c/(a2 + b2) Let A'B'C' be the circummedial triangle. Let A″ be the trilinear product B'*C', and define B″, C″ cyclically. A″, B″, C″ are collinear on line :ref:`X(798) <X(798)>\)X(812) (the trilinear polar of X(3112)). The lines AA″, BB″, CC″ concur in X(82). (Randy Hutson, October 15, 2018) X(82) lies on these lines: 1,560 10,83 31,75 37,251 58,596 689,715 759,827 X(82) = isogonal conjugate of X(38) <X(38)>`

Notes

Barycentrics a/(b2 + c2) : b/(c2 + a2) : c/(a2 + b2)

Let A’B’C’ be the circummedial triangle. Let A″ be the trilinear product B’*C’, and define B″, C″ cyclically. A″, B″, C″ are collinear on line X(798)X(812) (the trilinear polar of X(3112)). The lines AA″, BB″, CC″ concur in X(82). (Randy Hutson, October 15, 2018)

X(82) lies on these lines: 1,560 10,83 31,75 37,251 58,596 689,715 759,827

X(82) = isogonal conjugate of X(38)

X(82) = isotomic conjugate of X(1930)

X(82) = anticomplement of X(21249)

X(82) = cevapoint of X(1) and X(31)

X(82) = trilinear pole of line X(661)X(830)

X(82) = crossdifference of every pair of points on line X(2084)X(2530)

X(82) = perspector of ABC and extraversion triangle of X(82) (which is also the anticevian triangle of X(82))

X(82) = crosspoint of X(1) and X(31) wrt the excentral triangle