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K746
K746

∑ (-u + v + w) x (v^2 (u + v)^2 y^2 - w^2 (u + w)^2 z^2) = 0

with u:v:w = cosA/2:cosB/2:cosC/2

X(1), X(177), X(234), X(7707), X(10489), X(14596), X(16016), X(18886), X(18887)

K746 is the locus of P whose anticevian triangle is perspective with the Mid-arc triangle. See TCCT 6.14.

K746 is a pivotal cubic with rather complicated pole Ω, pivot P and isopivot Q.

SEARCH numbers : 0.233349142841901, 0.297544492506777, 2.15341840365918 respectively.

Peter Moses found rather nice barycentrics for these points (2018-06-01) :

Ω = X(18885) = Sin[A] Tan[A/2] (Cos[B/2] + Cos[C/2])^2::

P = X(18886) = Tan[A/2] (Sec[A/2] + Tan[A/2])::

Q = X(18887) = Sin[A] (Cos[B/2] + Cos[C/2]) (Sin[B/2] + Sin[C/2])::